Preheat grill to 300-400 degrees F (150-200 degrees C).
Place Portabella Mushroom Cap (2) on grill over indirect heat during preheating. These will take longer to cook than the burgers.
Meanwhile, divide 85/15 Lean Ground Beef (2 pound) into 8 portions and form into patties with hands. Use wax paper as surface to form patties. Make them fairly thin patties.
Form small circles of cheese that will fit inside the patties. White Cheese (4 slice) on 4 of the patties and sandwich the cheese with the other 4 patties on top.
Seal edges together by firmly pressing the ground meat with fingers, ensuring the cheese doesn't leak.
Grill burgers until done. Remove burgers and mushrooms.
Slice portabella caps into thin slivers. Place burgers on Onion Roll (4). Top with Shredded Parmesan Cheese (1/3 cup), mushroom slices, and Steak Sauce (to taste).
Make sure burgers have been cooling for at least 10 minutes so the cheese filling isn't boiling hot. Slice burgers in half if desired, or just serve whole for guest to bite into the cheesy surprise.