In a bowl, combine beef with 3 tbsp sauce and egg. Form into four patties.
Grill with lid closed, about 4 min per side or until cooked through. Top with cheese, if using, for the last 1 min of grilling.
Meanwhile, place mushrooms and butter in a Multipurpose or Round Steamer. Cover; microwave on high until tender, about 4 min. Add remaining sauce; cover and microwave on high for 1 min or until heated through.
To serve, place burgers on bottom bun halves. Generously spoon warm sauce over top. Add toppings, if desired. Cover with top bun.