How to Make It
In a large heavy cast iron or non-stick skillet over medium heat, cook the bacon until browned and crisp, about 8 minutes. Transfer the bacon to paper towels to drain and reserve the fat in the skillet in a small container.
In the same skillet, heat 1 tablespoon of the bacon fat over medium heat. Brown half the English muffins in the skillet, split-side-down, then transfer to a work surface. Repeat with the remaining English muffin halves and 1 more tablespoon of bacon fat.
Preheat the broiler. Place 1 slice of cheese on each muffin bottom and place under the broiler until the cheese is melted, 1 to 2 minutes.
In the same skillet, heat the remaining bacon fat over medium-high heat. Fry the eggs to desired doneness, about 3 minutes for runny yolks, then sprinkle each with a pinch of salt and pepper and divide the eggs between the English muffin bottoms. Top with the bacon slices and dress with mayonnaise and ketchup to taste.