Preheat oven to 425 degrees.

In a medium saucepan, melt butter over medium heat. Add in the flour, stirring with a wooden spoon continuously until smooth. At the same time, in a separate saucepan over medium heat, warm the milk. Pour the warm milk into the flour mixture, breaking up any lumps that appear. Stir until the sauce is thickened, approximately 3 minutes. Remove from heat and season with salt and pepper. Stir in nutmeg, half of the mozzarella and all of the Gruyere and Parmesan.

Return the saucepan to medium heat and stir until the cheese is melted, approximately 3 minutes. Keep warm over low heat.

Place slices of toasted bread on a lined, rimmed baking sheet. Spread Dijon over 4 of the slices, top each with slices of ham and some of the mozzarella. Top with the remaining slices of bread.

Turn oven to broil on low. Pour over the cheese sauce and top with the remaining mozzarella. Bake under the broiler for approximately 5 to 10 minutes, until the cheese bubbles and is browned. Serve immediately.