Preheat oven to 400°F. Line a baking dish, that has at minimum 1″ walls, with foil. In a large bowl mix together ground venison, steak sauce, and diced onions. Form into patties and place in the foil lined baking dish. Put sliced peppers in the spaces between the burgers. They will fry in the juices as the burgers bake. Bake for 20-30 minutes, until the internal temperature reaches 160°F and juices run clear (for either beef or venison). Flip the burgers once at their halfway mark. Add cheese slices for the last couple minutes of baking time.
Place on hamburger buns with your favorite toppings and condiments. Enjoy!