Preheat oven to 375°.
Mix the eggs, half-n-half, nutmeg, and salt and pepper. Set the mixture aside while you prepare the bread boats.
Depending upon the shape of the rolls, carefully cut a circle or square around the top and remove the crust.
Pull out excess bread to make a well. Do not cut through the bottom of the rolls or the egg mixture will leak out.
Add 1-2 tablespoons of cheese to the bottom of each roll.
Add 1-2 tablespoons of diced ham on top of the cheese.
Slow and carefully pour the egg mixture into each bread bowl.
Top with extra cheese and ham and bake for 20-25 minutes.