Combine venison, liquid smoke, and breadcrumbs in a bowl. Mix together thoroughly. Separate into 8 patties.
Place one patty on a cutting board and cover with slices of gouda cheese. Place second patty on top of the cheese and seal edges. You will be left with 4 completed burgers.
In separate bowl, mix mayonnaise, BBQ sauce and liquid smoke to create Fireworks sauce.
Place butter, onions, garlic and mushrooms onto tin foil. Curve the edges of tin foil to enclose the ingredients. Place enclosed ingredients on the grill. Grill until mixture is slightly browned and onions are translucent.
Salt and pepper burgers liberally and place them on grill. Cook to desired doneness.
Place finished burger and sautéed mushrooms and onions on brioche bun. Top with Firework sauce mix.