In a mixing bowl, whisk together eggs, a splash of milk, salt, and pepper until smooth and frothy.

Heat a nonstick skillet over medium heat and add a teaspoon of butter. Once melted, pour in the egg mixture and stir gently for about 3–4 minutes.

While the eggs cook, spread butter on one side of each slice of bread. Optionally, spread mayonnaise on the unbuttered side for extra flavor.

On the unbuttered side of one bread slice, layer cheddar cheese, scrambled eggs, bacon, and mozzarella cheese. Top with the second slice of bread, buttered-side up.

Transfer the sandwich to the skillet over medium heat. Cook for 3–4 minutes, then flip and grill the other side for another 3–4 minutes.

Remove from skillet, rest for a minute, then slice diagonally and serve hot, alongside hash browns or fresh fruit.