Preheat grill to medium-high heat, about 400 degrees F.
In a small bowl, combine the mayonnaise and 2 tablespoons of the sun dried tomatoes. Refrigerate.
In a large bowl, using your hands, combine ground venison, the remaining sun dried tomatoes, shredded mozzarella cheese, fresh chopped basil, worcestershire sauce, garlic powder, salt, and black pepper until just combined. Do not over mix.
Divide burger mixture into 6 equal portions and shape into patties.
Place burgers on hot grill and cook for 5-6 minutes on each side, until internal temperature registers 160 degrees F.
When burgers are almost ready, place slices of fresh mozzarella cheese on top of the burger and lower the grill lid to cook another minute until cheese melts.
Remove burgers from the grill and place on a plate. Allow burgers to set for 5 minutes before serving.
Serve burgers on grilled bread or burger buns and top with sun dried tomato aioli and fresh basil.