Spread mayonnaise and mustard on each slice of bread. Layer with a slice of cheese, ham, another slice of cheese, and top with bread.
Use a cutting board or the bottom of a frying pan to gently press the sandwich down.
Preheat a skillet or non-stick pan over low-medium heat. Melt the butter.
In a bowl, whisk together the milk, eggs, salt & pepper until combined. Dip the sandwich into egg mixture to coat both sides. Add sandwich to the pan and cook for 4-6 minutes, then flip and cook for another 4-5 minutes or until melted and golden brown on each side.