One of the things I do is to keep track of generic professorial skills and a real world descriptive of how skilful said NPC is in that skill. The skill could be such as soldier, cleric, terrorist, spy, mathematician. The descriptives can range from poor to legendary. If during game play you need to add more skills, or refine one of them then a quick note is all you need.

For example: Bob the assassin has an assassin skill of good. He's good at all things that an assassin is supposed to be. Fred the bar keep may have a bar manager skill of poor (thus why he is always asking the PCs to help) but a performance skill of legendary (thus why the parties at his place are legend ... wait for it .. DARY!

Depending on how rule heavy you want to be, those skill could get more and more focused. But the more focused the skill, the more skills you have to write.

Note that those familiar with Over The Edge may recognise this system as extremely similar and they would be right.

Official Stats are in Volo's Guide to Monsters

Volo's Guide to Monsters (released November 2016) includes many additional Illithid variants and related creatures. One of these is the Elder Brain.

The official Elder Brain description can be found on pages 173 and 174 of Volo's Guide and includes lair actions, regional effects, a full stat block, and lore on the nature of the Elder Brain.

But Matt Mercer's Elder Brain is homebrewed

Matt Mercer's Elder Brain appeared well before the publication of Volo's Guide, and thus is distinctly homebrewed. Additionally, Matt himself has stated:

...and at full strength [the Elder Brain] is a CR 20 creature.

This doesn't line up at all with the official publication, which only has a CR of 14. A quick search didn't turn up any exact stats for his Elder Brain, only a meager collection from the third party critical role stats site which has the following information:

• Elder Brain First Appearance: 10 K’Varn Revealed
• Armor Class 18 (at weakest), 20 (before party flees)
• 320 damage taken and “not on death’s door yet”