Place chicken breasts between sheets of plastic wrap and pound with a meat mallet to a uniform thickness of 0.25 inches.
Season both sides of the chicken with salt and black pepper.
Layer one slice of ham and one slice of cheese on each breast, leaving a 0.5-inch border around the edges.
Roll the chicken tightly, starting from the small end, and secure with toothpicks or wrap tightly in plastic wrap and refrigerate for 15 minutes to set the shape.
Preheat oven to 400 degrees Fahrenheit (204 degrees Celsius).
Prepare a breading station with three bowls: flour mixed with garlic powder and onion powder; beaten eggs; and panko mixed with smoked paprika.
Dredge each roll in flour, dip in egg wash, and coat thoroughly in panko, pressing firmly to ensure maximum adhesion.
Place rolls on a wire rack set over a baking sheet and bake for 20-25 minutes until the internal temperature reaches 165 degrees Fahrenheit.
For the sauce: Melt butter in a saucepan over medium heat, whisk in 2 tablespoons of flour and cook for 1 minute without browning.
Slowly whisk in milk and simmer until thickened to a coating consistency.
Whisk in Dijon mustard and Parmesan cheese until smooth; season with salt and pepper.
Remove toothpicks from chicken and serve immediately topped with the warm Dijon cream sauce.