Fry the bacon strips in a skillet over medium heat until they turn crispy and golden, about 5-7 minutes. Transfer them to a paper towel-lined plate to drain excess grease.

Whisk together the eggs, milk, and black pepper in a bowl until well combined. Pour the mixture into the skillet with the remaining bacon grease and cook gently over medium-low heat, stirring for about 3-4 minutes until softly scrambled. Set aside.

Layer cheese on four slices of sourdough bread, spreading it generously. Place the crispy bacon and fluffy scrambled eggs on two of the slices, topping them with the remaining slices to create sandwiches.

Butter the top of each sandwich with unsalted butter. Heat a clean skillet over medium heat, then place the sandwiches butter-side down into the skillet.

Cook for 3-4 minutes until the undersides are golden brown and crispy; gently press with a spatula for an even toast. Butter the tops, then flip the sandwiches and cook for another 3-4 minutes until golden.

Cool the sandwiches for a minute before slicing them. Serve immediately and enjoy the mouthwatering flavors!