In a bowl, beat the eggs with salt and pepper to taste. Mix with the whole milk. Place a slice of cooked ham between two slices of cheddar cheese and make a sandwich with two slices of bread. Let the sandwich soak in the egg / milk mixture for a while. Melt a nut of butter in a Mesana Magefesa electric grill over medium heat. Before the butter starts taking color, arrange the bread slices on the griddle and let brown over low heat. This way the heat will penetrate slowly to warm the interior, melting the cheddar cheese.