So, I've decided to go back to CK2 (I have been doing a multiplayer game with friends for more than a year - started in 769, we're currently in ca 1060 - and all of a sudden I started craving more CK2). I've started 7 ironmen, all with different start dates: 867, 936, 1066 (William the Conqueror bookmark), 1081, 1187, 1241, 1337.
Religion split is pretty good: two of these are as a catholic, two as a sunni, two as pagans (but I don't plan to reform - in fact pagan reformation is disabled in one of those) and one as a buddhist.
I've finished the 1241 one, which was awesome (I'm going to try to AAR this) and because I liked it I decided to also quickly wrap up the 1337 playthrough, which went quickly but was still fun. It's more of a kingdom than an Empire, but I'll post it here regardless. (starting in 1337, it's hard to build a huge empire - not a lot of time, a lot of well established kingdoms).
Started as the count of Vienne, Ubert de la Tour du Pin. One county, vassal of Savoy (in the middle of France and the HRE). And I can present you....

The Kingdom of Arles and the wider HRE in 1453 (and yes, Denmark is part of the HRE - note that Italy isn't). The Kingdom of Arles (bottom left, granate color) is part of the HRE, as it should be. Note that the king of Arles is also duke of Silesia, hence the granate part near Poland. Arles is one of the Emperor's most important vassals (upon exporting to EU4, Arles is elector).
To get there, I first rebelled against the duke of Savoy to join the kingdom of France, who in 1337 owns the last 3 counties of Dauphiné (the de jure duchy of Vienne). I then quickly fabricated claims and invaded the counties of Lyon and Vivarais.... but these two counties are owned by bishops in 1337, so because of their church capital they were worthless to me ! And then drama, soon before I won the war against Vivarais, the king of France created the duchy of Dauphiné and gave it to the count of Forez (a vassal of Burgundy at the start). The count of Forez also owns a barony in Lyon, so my new liege was decently powerful compared to me, who owned two useless bishoprics. The end of the reign of my starting character and my second character's reign were.... uneasy, and then came this guy:

This guy single-handedly made the kingdom of Arles. With him, I managed to claim the duchy of Dauphiné AND the county of Forez as my owns, leaving the former dukes of Dauphiné to rot in their last barony. Then, thanks to his absurd intrigue I murdered the king of France so that the king's young son would inherit. The king of France having created the kingdom of Arles (notably thanks to my conquest of half of Savoy in an unremarkable war), I decided to plot to claim it but I screwed up (didn't know you had to go trigger a decision in the intrigue panel - yes, I'm dumb). So I murdered the new king of France as he started to approach adulthood, getting caught in the process but who cares about general opinion ? In the meanwhile I had gone crusading because at the first crusade I had said "yes yes, I'll go" without going to the Pope, who excommunicated me in return. So I decided to actually go this time and conquer a barony - except the crusade was successful, leaving one of my dynasty member as a duke in the newly catholic kingdom of Maghreb (had the option to play as him but declined) and seemingly gaining a lot of gold from this (though the assassination of a couple barons, so I could inherit their baronies and Lyon and Vivarais became counties with a proper barony as capital, might've helped me gain gold too).
With this gold, and the willingness of the Pope to give me a claim on the duchy of Provence, I went to war with Naples and overwhelmed them with mercs. Now rather powerful, I decided it was time for me to join the more decentralised HRE, so I set up an independance faction thinking that the new, young and weak king of France would not oppose me. He foolishly did, but again mercs stacks took care of him. So then I joined the HRE, having enough lands to usurp the kingdom of Arles and being crowned by the Pope. This character did not enjoy it for long, dying 2 years into his reign while trying to forge a bloodline, and his mediocre successor (who is the character with whom I finished the game) ascended to the throne, crowned by the Pope too. Not much to report since, outside of a war with Switzerland to gain control of the rest of Savoy.

The outside world in 1453. Maghreb, Jerusalem, Arabia and Egypt are catholics. Maghreb, Arabia and Egypt, thanks to regular crusades. Jerusalem was established by the children's crusade - in all of its events I decided to give him as much support as I could, because I found it fun. Except for the last one, where he asked for me to join his war to establish Jerusalem. Then I merely prayed for his success - but it looks like it was enough ! The king went cathar later in his life, but he died before spreading it much and his son is a regular catholic (a cathar Jerusalem would've been fun, though). The muslims mostly survive in India and Mali, outside of a couple emirates in Northern Africa - the Ilkhanate (still here as the green Persian blob) went buddhist. Ireland exists because England created it and lost it. Now the Plantagenets only own Ireland, while the crown of England went to the de Barcelona and later to another catalan dynasty. The king of Egypt is also married to my daughter and heir, so that would make for an interesting future