1. Prepare the Chicken
Preheat your oven to 375°F (190°C).
Place each chicken breast between two sheets of plastic wrap or parchment paper. Use a meat mallet or rolling pin to pound the chicken to an even thickness of about 1/4 inch.
2. Assemble the Roll-Ups
Lay the pounded chicken breasts flat on a clean surface. Place two slices of ham and two slices of Swiss cheese on each chicken breast.
Starting from one end, tightly roll up each chicken breast and secure it with toothpicks if needed.
3. Coat the Roll-Ups
Set up a breading station with three shallow bowls: one with flour, one with beaten eggs, and one with bread crumbs mixed with garlic powder, onion powder, salt, and pepper.
Dredge each chicken roll-up in flour, shaking off any excess. Dip into the beaten eggs, then coat thoroughly with the seasoned bread crumbs.
4. Bake the Roll-Ups
Place the coated chicken roll-ups in a greased baking dish. Drizzle with olive oil or melted butter.
Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and the outside is golden brown and crispy.
5. Prepare the Sauce (optional)
While the chicken is baking, make the sauce: In a medium saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes until bubbly and lightly golden.
Gradually whisk in the milk and chicken broth, cooking until the mixture thickens and comes to a simmer.
Remove from heat and stir in the shredded Swiss cheese until melted and smooth. Season with salt and pepper to taste.