Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.

Place each chicken breast between sheets of plastic wrap and pound with a meat mallet to a consistent 1/4-inch thickness.

Season both sides of the chicken with salt and pepper. Layer one slice of ham and one slice of cheese onto each breast, leaving a 1/2-inch border at the edges.

Tightly roll the chicken from the narrow end to the wide end. Secure the seam with wooden toothpicks to maintain the shape.

Set up a breading station with three shallow bowls: one with flour, one with the egg wash, and one with Panko mixed with garlic powder and paprika.

Dredge each roll in flour, dip into the egg wash, and coat thoroughly with the Panko mixture, pressing gently to ensure adherence.

In a large oven-safe skillet, melt 2 tablespoons of butter over medium-high heat. Sear chicken rolls for 2 minutes per side until the exterior is golden brown.

Transfer the skillet (or move rolls to the prepared baking sheet) to the oven. Bake for 20-25 minutes until the internal temperature reaches 165°F (74°C).

While chicken bakes, prepare the sauce: Melt 3 tablespoons of butter in a small saucepan over medium heat. Whisk in 3 tablespoons of flour and cook for 1 minute to create a roux.

Gradually whisk in milk and chicken broth. Simmer for 3-5 minutes, whisking constantly, until the sauce thickens and coats the back of a spoon.

Stir in the Dijon mustard and Parmesan cheese until melted and smooth. Remove from heat and adjust seasoning with salt and pepper.

Remove toothpicks from the cooked chicken and serve immediately, drizzled generously with the velvety Dijon sauce.