In a bowl, whisk together the eggs, milk, salt, and pepper. Heat a non-stick skillet over medium heat and scramble the eggs until soft and fluffy. Remove from heat and set aside.
Butter one side of each bread slice. On the unbuttered side of two slices, layer cheddar cheese, scrambled eggs, bacon or sausage, and mozzarella cheese. Top with the other slices of bread, buttered side facing out.
Heat a skillet or griddle over medium-low heat. Place the sandwiches in the pan and cook for 3-4 minutes per side, pressing down gently, until the bread is golden brown and crispy and the cheese is fully melted.
Remove from the pan, let it cool for a minute, then slice diagonally. Enjoy with ketchup, hot sauce, or maple syrup for a delicious twist!