Preheat your oven to 350°F (175°C).

Place chicken breasts between two sheets of plastic wrap and pound to 1/4-inch thickness. Season with salt and pepper.

Lay a slice of Swiss cheese and a slice of cooked ham on each chicken breast and roll tightly, securing with toothpicks.

Set up your dredging station with flour, beaten eggs, and panko breadcrumbs in separate shallow dishes.

Dredge each chicken roll in flour, dip in eggs, and coat with panko breadcrumbs.

In a skillet, heat butter and olive oil. Brown the chicken rolls for 5 minutes on each side.

Transfer the browned chicken to a baking dish and bake for 20-25 minutes until cooked through.

Prepare the cream sauce in the same skillet by melting butter, whisking in flour, and gradually adding milk until thickened. Add Parmesan and Dijon mustard.

Serve the chicken rolls with the warm cream sauce drizzled on top.