Set an oven rack 6” below the broiler. Preheat broiler to high.
Arrange 2 ham slices in a circular fashion on a non-stick baking sheet. Top the ham with 3 slices of tomato. Repeat with the remaining ham and tomatoes. Broil 2 minutes, and then turn off the broiler. Top the tomatoes and ham with the cheese and keep warm in the oven.
Set a non-stick skillet over medium-low heat. Set 2 egg rings (see Note) in the skillet and lightly coat with vegetable oil spray. Crack an egg into each egg ring. Break the yolks, if desired. Cover the pan and cook until the eggs set, about 3 minutes.
While this occurs, toast the English muffins and spread with mayonnaise. Sandwich the lettuce, egg, ham, tomatoes and cheese between the English muffins and serve.
Note: Egg rings are designed for cooking eggs perfectly round and are available at kitchenware stores. If you can’t find one, simply fry the eggs as you normally would.