In my own experiences, the key to writing essays quickly and expertly is just writing a lot of essays and consciously trying to hone your craft. Writing is a complex skill that takes lots of time and attention in little incremental steps, and the further you go the faster/better you get.

It's more than just practice though. It's also momentum. I find that the more I write, the more my brain passively seeks more material to write, and so I get faster at generating ideas and putting them on paper. This happens with programming too - the more I do, the faster I get at coming up with ideas and prototyping them. Same with sports, gaming, really everything that combines skill and creativity. I get more creative by just doing it more.

Certainly there's real technique to writing quickly, but I've always found that my own biggest barrier was having something meaningful to say, and the fastest way to get into a rhythm of actually coming up with meaningful things to say was to just start putting words down in the first place. Which leads to the paradox: you become prolific by trying to be prolific.