Season ground beef with salt, pepper, and garlic salt according to taste. Make into patties and cook until done.
Grill sliced onions in butter until tender. Spread butter on bread and brown, buttered side down, in skillet. When toasted, turn bread over and place a slice of Monterey Jack cheese on one slice of bread and a slice of Mozzarella cheese on the other. Put a beef patty on one side; top with grilled onions, then top with other side of bread and cheese. Flip sandwich as when making grilled cheese to completely heat cheese.