Croque Madame

Name: Croque-Madame
Ingredients: 7 tablespoons softened unsalted butter, divided; 1 tablespoon all-purpose flour; 1/2 cup milk; 1/4 teaspoon kosher salt, plus more for serving; Dash freshly grated nutmeg; 3 tablespoons fresh grated Parmesan cheese; 6 ounces sliced or grated Gruyere cheese, divided; 4 slices bread; 2 to 3 teaspoons Dijon mustard, optional; 4 ounces thinly sliced ham; 2 large eggs; Dash freshly ground black pepper, to taste