The divergences pick up, and quickly, and in many places - for early 15th century was an unstable and dangerous, and, as Sapkowski described it, historic time.
"How can we tell that a time is historic? Simple. Everything is happening way too fast."
Take, for instance, the Hundred Years War, which for thirty years was very very quiet. Suddenly - bah! - in 1407 a mini-civil war started in France between Armagnac and Burgundian dukes, while the king was raving mad. And then, in 1415, an English army landed in northern France. The awesome Armagnac French heavy cavalry force, the finest in the world, [insert more aristocratic French propaganda here], has rode to meet the English at Agincourt, knowing that the poor stupid English peasants would probably run away when the first charge comes. Yay!
The French knights were a rather excitable bunch, and very emotional, too. And impatient. The silly mercenaries can't even move properly, they are supposed to charge, not move like a bunch of turtles! The French knights destroyed the formations of their own infantry and charged to victory and glory. Victory and glory of the English. The French knights, as far as I know, were rather surprised to find themselves dead or captured.
After that great English victory, Anglo-Burgundian forces waited until 1417, for some reason. When it did come, they charged across France very very fast. Maybe, maybe the French could have gathered forces and put up serious resistance, but a) that was unlikely in the first place and b) the Holy Roman Emperor was feeling pro-English, while Duke Gian Galeazzo Visconti, an ever-loyal ally of the Holy Roman Emperor and much like most remaining Italian rulers a man with a good sense of profit, went on a rampage. Oh, Genoa? You are trying to help the French? No, your imperial majesty, don't intimidate them like in OTL and let me teach them a lesson! Take that, Genoa! Genoa fell, much to the cheers of the Venetians who discarded their fear of the Milanese. After all, they killed Genoa, surely that means that they're nice people!
Provence is ruled by relatives of the French king, who sympathize with that madman! Bah, they're hardly good vassals of your imperial majesty. There, let me liquidate that little inconvenience. Take that, Provence...
Etc. Suffice it is to say that the Milanese also by then grabbed up Genoa after a very violent assault augmented with good use of cannons, granted Provence to the Holy Roman Emperor (who was so touched and who so didn't want such a distant possesion that he awarded it to his most loyal vassal, Duke Visconti), then finally attacked France. Charles the would-be VII, the heir to the French throne, was called a dauphin for his holdings in Dauphine. Luckily for himself, he wasn't there in 1419, because that's when the mercenary armies of Milan overrun the whole region with Imperial help. The dauphin was smarter then his father and realized that, basically, he was losing this. But the peace terms were to exclude him and his family from the line of succession to the French throne ALTOGETHER and forever. Amongst other nasty things. He sighed, and decided to fight on. But the French were losing and losing, even after mustering something of an army. That army was crushed in 1423, when the Anglo-Burgundian forces took Orleans. Further south, Languedoc was occupied by the Milanese; of little relief was the fact that after this, the Milanese stopped the major offensives and instead started pillaging nearby territories. In 1426, in the Battle at Limoges, the dauphin was captured. This was the end. The Hundred Years War was over.
What came in its place? Well, first there was a now-connected (by French territory) Burgundy somewhat to the east of the Seine (and also slightly east from Paris). it stretched from Flanders to Franche Comte and Vichy. The Milanese have taken over Genoa (including Corsica), Dauphine and Provence. The rest became a part of the new United Kingdom of England and France. Ofcourse, there will be some qualms with this, the largest being the "Holy Rebellion" or "Joan the Witch's Uprising" (depending on your point of view), raging from 1429 to 1437, and that's not counting the small rebel groups that were left over from that rebellion well into the 1450s. There were rebellions, yes. But King Edward V of England, or Edward I of the United Kingdom as he is more popularily known, or rather Edward the Unifier, or Edward the Conqueror, or the ever-fashionable Edward the Great, didn't let anything of the kind to overthrow him.
Burgundy prospered from this in particular, becoming a kingdom within the Holy Roman Empire. The first king was Philipp I the Good; under his reign, Burgundy would not only become a kingdom, and not only a fairly big one, and not only a very rich (due to Flanders) one, but also would gain would gain the lands of Brabant and Holland, and become very influential. Future historians would describe Burgundy and Milan as treacherous children of the Holy Roman Empire, under whose fatherly protection they prospered until they were strong enough to act on their own, not giving anything back to poor, poor Holy Roman Empire.
Notably, those future historians did not come from neither Burgundy nor Lombardy (as Milan would later be known as. Some wanted to call it Italy, but they-who-be-in-power decided that as England wasn't Britain and France wasn't Gaul and Hungary wasn't Pannonia, Lombardy shouldn't be Italy, case closed)... They WERE however from [insert a nation in this world's future that doesn't like neither Lombardy nor Burgundy].
Much like in OTL, the Hussites rebelled in 1419, causing a lot of trouble and distracting many of their neighbhors to sending hordes of knights to put the followers of Hus down. Much like at Agincourt, the knights were rather rudely beaten up. Eventually, as Poland was unstable and unable to send reinforcements, Zizka succesfully fought back the crusaders. A very awkward peace left the Hussites in control of Bohemia and Moravia, though after Zizka died from the plague, a more moderate faction came to power. After quite some hassle, they elected a monarch from local nobility (the part of it that didn't flee) starting the Varic Dynasty and declared the Hussite Church to be the state religion. That caused another crusade, though a much smaller one. All crusaders involved were injured in the making of this timeline. As time went by, trade restarted with Poland and other neighbhors...
Because I say so, the Hohenzollerns never did get Brandenburg (butterflies from different Imperial policies and some other stuff), concentrating on Franconia instead.
In the year 1410, met two armies at Grunwald-Tannenberg. On one side, the Poles, with various mercenaries and other such folks, though not getting the promised Lithuanian reinforcements, on the other side, the Teutonic Order. Now, normally this would have been yet another triumph of infantry over cavalry, but it just so happened that the Teutonic Order also had Novgorodian mercenaries. And other mercenaries as well. Also, the Poles too did not overtly rely on infantry yet. So the Polish forces were eventually routed; the last one to retreat were the Czech mercenaries. Amongst them was Jan Zizka, but this name hardly meant anything to anybody before 1419.
Either way, the Teutonic Order prolonged its existance...
Lithuanian armies marched east, on and on. By 1430, all the old lands of the Golden Horde were safely in their hands after Tokhtamysh was poisoned. In 1432, a great war started with Muscovy, in 1433, the Muscovite forces were crushed at Tushino. By 1440, Novgorod also was subdued, as were the various minors. The Lithuanian-and-Russian Grand Duchy, or the Grand Duchy of Lithuania-Russia, has united Russia. While religious tensions between west and east remained in the Duchy, these were not too violent. Trully Lithuania-Russia had great potential...
The Ottomans in 1413 under Muhammad I have once again raised their head, using the instability in the Timurid Empire in order to start grabbing the tiny Anatolian states. But Shah Rokh didn't like that, for some reason. By 1417, he was done with internal threats and rebellions. I don't have much time, so I'll be brief. By 1426, after a very close battle, the Ottoman forces were crushed. By 1430, Anatolia was divided between Timurid vassals, while the Sultan fled to the Balkan Ottoman territories. But there, Hungary, now freed up from the Hussite Crusades, invaded, conquering many lands and installing many puppet rulers. By 1440, Ottomans were no more, Byzantines controlled the entire Marmara coast and parts of Thrace, Bulgaria was independant, while West Balkans up to the Latin and Byzantine states in Greece was under Hungarian rule, direct or indirect. Ofcourse, getting there involved some wars with the local population...
A not in particular significant (or so it seems!) change happened in China. The capture of the Yung-lo Emperor by the Mongols shook him up seriously, and thus long-distance sea travel was cancelled earlier - in 1415. However, his capture also seriously damaged his health, and the imperial administration system as well. Generally, this meant that Ming China got more unstable then in OTL...
