Step 1Cook the bacon until crisp, drain on paper towels and set aside.
Step 2Place the slices of cheese on one slice of the toasted bread and place in a toaster oven or under a broiler to melt the cheese.
Step 3Spread the other slice of toast with the mayonnaise, top with the cooked bacon, the sliced tomato and the lettuce.
Step 4In a nonstick skillet, melt the butter over medium heat. Fry the egg, turning over briefly when the bottom is set. (Keep the yolk runny.)
Step 5Slide the finished egg on top of the lettuce. Top with the other slice of toast, melted cheese side down. Place the sandwich on a plate and slice in half, letting the yolk run down the sandwich.