This is the cook book on Amazon (they don't offer it directly on their site), and this is the famed restaurant in question.
I'm not going to go through the entire recipe, as there are hundreds of solid vegan sloppy joe recipes for free online (or you could even use a standard one and just use something other than meat) and I think people should pick-up their book.
My changes were mostly seasoning based, regarding my personal tastes and what was on hand in the house. But their technique was very straight forward to anyone experience with cooking. Dice and sweat and slightly brown your aromatics, temper in any dry spices and cook the rawness off of any pastes, add in the wet ingredients, deglaze, simmer and reduce. Simmer protiens for at least 10 minutes in finished sauce. Adjust seasoning and acid to taste. 100% standard procedure for anything stew or chili-like, or being concentrated down to sauce or gravy like coating.
I definitely used some fermented chili pastes instead of just chili powders for extra depth, and dialed back the sweetness of their recipe a bit (the sweet level in theirs is still good and perfectly appropriate for a classic sloppy joe, but when you're cooking why not make it your own ideal?)
The other big change was choosing to use primarily textured vegetable protein for the "meat" (along with some fresh tofu) where their recipe calls for all fresh tofu.
They also top theirs with crunchy deep fried onions. I LOVE having fresh crispy well fried onions or shallots on hand (don't even bother with storebought) but it is a bit of project to do at home without the benefit of fryolator and it wasn't the right evening to add that to this meal. So I topped it with Fritos corn chips which definitely fits with the cheap, trashy (that's meant very lovingly here), comfort food that a sloppy joe is.