Preheat the oven to 375° F.

Crack eggs into a medium size bowl, add milk, salt and pepper and whisk vigorously until homogenized and frothy.

In a medium-size, non-stick sauté pan, heat the butter over medium- low heat. Add the egg mixture and the ham and let sit until the eggs start to set around the edges. Using a rubber spatula, move the eggs from the outside to the center. Once the outer edges begin to set, move to the center. Continue this process until the eggs are almost set. The eggs should be slightly wet. Divide the egg mixture between the two bottom halves of the croissants.

Divide the cheese between the two top halves of the croissants. Transfer the croissants to a baking sheet and place in the oven. Bake until the cheese is melted, about 4 to 5 minutes. If not serving immediately, wrap the sandwiches in aluminum foil.

To reheat the sandwiches, place in a 350°F oven for 5 minutes or until warmed through.