Prepare the Burger Patty: Season the ground beef with salt and black pepper. Shape the meat into a patty slightly larger than a slice of bread. In a skillet over medium heat, cook the patty for about 4-5 minutes on each side until cooked to your desired doneness.

Prepare the Grilled Cheese: Spread mayonnaise on one side of each slice of bread. Place a slice of cheese on the mayonnaise side of each of two slices of bread.

Assemble the Sandwich: Place the cooked burger patty on one slice of prepared bread with cheese. Add tomato slices and optional onion rings on top of the patty. Top with the second slice of prepared bread with cheese, mayonnaise side down.

Grill the Sandwich: In a clean skillet, add butter and melt over medium heat. Place the sandwich in the skillet and grill for about 2-3 minutes per side, until the bread is golden brown and the cheese is melted.

Serve: Remove from heat, slice diagonally, and serve with ketchup for dipping.