Spread ½ tablespoon of mayonnaise over one side of each slice of bread.
Place ¼ cup of cheese on the bottom slice of bread. Next, add 1 slice of the bacon and top with 1 tablespoon of cheese. Layer two tomato slices on top of the cheese and top with 1 more tablespoon of cheese. Top with 1 more bacon slice and 2 more tablespoons of cheese. Repeat this step for all 4 sandwiches.
Place the sandwich on the grill and cover with the second slice of bread. Cook on medium low for 3 minutes, or until sandwich is golden on the bottom and the cheese is melting.
Flip the sandwich and cook for another 3 minutes, or until golden brown and cheese has melted. Press the sandwich with a small heavy cast iron pan if needed to aid in the cheese melting.