Crisp bacon slices in a skillet; set aside.
Assemble sandwiches with bread, cheddar cheese slices, and cooked bacon.
Whisk eggs, milk, and salt together in a shallow wide bowl.
Melt butter in a skillet over medium heat.
Dip assembled sandwiches into the egg batter coating both sides, then pan-fry for 3 minutes per side until golden brown and cheese melts.