Toast the bread slices in a toaster or skillet until golden brown on both sides.

Whisk the eggs, milk, salt, and black pepper in a bowl until well combined.

Melt the butter in a nonstick skillet over medium heat, pour in the egg mixture, and scramble gently for 2 to 3 minutes until soft curds form.

Place 2 cheese slices on the eggs in the skillet, turn off the heat, and let the cheese melt for 30 seconds.

Divide the cheesy scrambled eggs between 2 toasted bread slices, top each with the remaining bread slice, and serve immediately.