Melt butter in a medium skillet over medium heat. Add onions and garlic until onions are translucent. Stir in mushrooms and saute until soft. Transfer to a medium bowl and allow to cool.
Add ground venison, blue cheese, breadcrumbs, salt and pepper and mix well with your hands to blend.
Form into 4 large patties. Grill, pan-fry or broil patties until browned. Add to bun with lettuce, tomato and your choice of other condiments.