Puree the onion in a food processor. Add meat, black pepper, cumin, coriander, oregano, garlic powder, and paprika, and pulse until incorporated, scraping down the sides as needed.
Place the meat onto a piece of foil or parchment and form into a log. Tightly wrap it.
Transfer the log of meat to the freezer and let it sit for 5 hours or overnight.
To cook:
Remove it from the freezer and carefully slice it into thin strips.
Over medium-high, heat some oil or vegan butter in a pan and in batches cook slices in a single layer, on both sides, until browned.
Build your Sandwiches:
Smear sauce of choice on a warmed flatbread, then top with lettuce, tomato, cucumber, and red onion.
Add kebab meat and drizzle with sauces of choice, and sumach, if using.
Roll up the pita and wrap it with foil to hold it together more easily. Or serve flat on a plate and follow guests or fam to roll it up themselves.