Place each chicken breast between plastic wrap or parchment. Use a meat mallet to pound to even 1/4-inch thickness. Season both sides with salt and pepper.

Lay each flattened breast on a clean surface. Place one slice of ham on each, followed by one slice of cheese. Keep fillings centered with 1/2-inch border around edges.

Starting from the shorter end, roll each breast tightly around the filling. Secure with toothpicks or tie with kitchen twine at 1-inch intervals.

Set up breading station with three shallow dishes: flour in first, beaten eggs in second, breadcrumbs in third. Dredge each roll in flour, coating completely and shaking off excess.

Dip floured roll into beaten eggs, turning to coat all sides. Let excess drip off, then roll in breadcrumbs, pressing gently to create even coating. Ensure complete coverage.

Place breaded rolls on greased baking sheet with space between them. Brush each roll generously with melted butter.

Bake at 375°F for 25-30 minutes until coating is golden brown and internal temperature reaches 165°F. Cheese should be melted inside.

Remove from oven and let rest for 3-5 minutes before removing toothpicks or twine. This allows juices to redistribute.

For optional Dijon cream sauce: Whisk together cream, Dijon mustard, and pinch of salt in small saucepan over low heat. Warm gently, stirring constantly, until smooth and heated through. Don't boil.

Slice each roll into 1-inch rounds to show spiral of ham and cheese. Arrange on plates, drizzle with optional sauce, and garnish with fresh parsley.