In a skillet over medium heat, cook the bacon until crispy, about 5-7 minutes. Remove and drain on paper towels.

In the same skillet, add butter and let it melt. Crack the eggs into the skillet, season with salt and pepper, and cook to your desired doneness (sunny-side up or scrambled).

Toast the bagels or bread. Place a slice of cheese on the bottom half, add the cooked bacon, then the egg, and top with another slice of cheese. Close the sandwich with the top half of the bagel or bread.

Return the assembled sandwich to the skillet and cover for 1-2 minutes to melt the cheese.