Preheat grill to medium-high heat or preheat broiler.
Combine 1/2 cup cheese, green onions and bacon; mix well and set aside. Combine meat, salt, pepper and remaining 3/4 cup cheese, mixing well. Shape mixture to form 8 thin patties 4-1/2 to 5 inches in diameter.
Divide cheese and green onion mixture over 4 of the patties; top with remaining patties. Pinch edges together well to seal.
Grill or broil 5 to 6 minutes per side or until internal temperature of meat is 160°F. Serve in rolls with lettuce, tomato and condiments as desired.