Heat oil in a large frying pan or heavy-bottomed pot over campfire or camp stove. Add venison, celery, onion, and pepper. Cook until meat is fully browned and vegetables are soft.
Add tomato sauce, ketchup, bbq sauce, brown sugar, Worcestershire sauce, vinegar, and mustard to pan. Cook until mixture thickens, stirring occasionally, about 25 minutes. Be careful not to let the sauce burn to the bottom of the pan.
Season with salt and pepper to taste. Sever over toasted brioche bun.
Notes
Note: Venison is an extremely lean meat. No need to drain fat after browning like you would for beef.