Combine ground beef, onion, Worcestershire sauce, mustard, garlic, salt and pepper in bowl with your hands. Shape into 1/2-inch thick patties. Poke a hole in the center of each patty. Place piece of cheese in hole and form meat into patty around cheese. Season with salt and pepper.
Brush grill with oil. Cook burgers, 3 to 5 minutes per side, or until meat thermometer inserted in side of burger reaches 160F. Meanwhile, toast buns on the grill 1 to 2 minutes. Serve with your favorite burger fixings.