Preheat your oven to 350°F (175°C).

Pound boneless, skinless chicken breasts to an even thickness of about ¼ inch, season with salt and pepper, then layer Swiss cheese and ham. Roll tightly and secure with toothpicks.

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

Coat each chicken roll in flour, dip in beaten eggs, and roll in panko breadcrumbs until fully covered.

Heat butter and olive oil in a skillet, sauté the breaded chicken rolls for about 5 minutes until golden brown.

Transfer chicken rolls to the baking dish, bake for 20 to 25 minutes until chicken reaches 165°F (74°C).

Prepare the creamy sauce by melting butter in a saucepan, whisking in flour, then gradually adding milk until thickened. Stir in Parmesan cheese and Dijon mustard.

Serve the chicken rolls on a platter, drizzle with creamy sauce, and garnish with fresh herbs if desired.