Prepare the Chicken
Place each chicken breast between two sheets of plastic wrap or parchment paper and use a meat mallet to pound it to an even thickness (about 1/4 inch).
Lay a slice of Swiss cheese and a slice of turkey or chicken ham on each flattened chicken breast. Roll tightly from one end to the other, tucking in the sides to seal. Secure with toothpicks if needed.
Bread the Chicken
Set up a breading station with three bowls: one for flour mixed with salt, pepper, garlic powder, and paprika; one for beaten eggs; and one for breadcrumbs.
Dredge each chicken roll in the flour, dip in the egg, and coat with breadcrumbs.
Cook the Chicken
Preheat your oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Sear the chicken rolls until golden brown on all sides, about 3-4 minutes per side. Transfer to a baking dish and bake for 20-25 minutes, or until the internal temperature reaches 165°F (74°C).
Make the Swiss Cheese Sauce
In a small saucepan, melt butter over medium heat. Whisk in the flour and cook for 1-2 minutes to create a roux.
Gradually add milk, whisking constantly until the mixture thickens. Stir in shredded Swiss cheese until melted and smooth. Season with salt and nutmeg, if desired.
Serve
Remove toothpicks from the chicken rolls. Drizzle with the creamy Swiss cheese sauce and garnish with parsley if desired.