Mix egg, milk, sugar, and salt in a shallow dish to make the egg mixture. Soak bread slices in the mixture for 5 minutes, flipping occasionally until fully absorbed.

Heat olive oil in a pan over medium heat. Cook bacon slices until browned on both sides. Sprinkle with pepper and set aside.

Wipe the pan clean with a paper towel, then melt butter over medium heat. Add soaked bread slices and cook until golden brown on both sides. Remove from the pan.

Sprinkle shredded cheese evenly in the pan over medium heat. Once the cheese starts melting, place the cooked bread slices on top. Cook until the cheese becomes crispy.