Preheat the oven to 400°F. Spray a 9x13-inch baking dish or large baking sheet with nonstick cooking spray.
Place 6 boneless skinless chicken breasts between two sheets of plastic wrap. Gently pound each breast to ¼ to ½-inch thick using a meat mallet or rolling pin. Be careful not to pound too hard or the chicken may tear.
Arrange the chicken on a clean work surface and season both sides with ½ teaspoon salt and ½ teaspoon black pepper.
Place 1 thin slice of ham and 1 slice of Swiss cheese on each chicken breast.
Roll each chicken breast tightly and place it seam-side down.
In a shallow bowl, whisk together 2 large eggs.
In a separate shallow bowl, combine ½ cup breadcrumbs, ½ cup panko breadcrumbs, and ¼ cup grated Parmesan cheese.
Dip each chicken roll into the beaten eggs, coating all sides, then roll it in the breadcrumb mixture until completely coated. Gently press the breadcrumbs onto the chicken to help them adhere.
Place the coated chicken rolls seam-side down in the prepared baking dish.
Lightly spray the tops of the chicken with nonstick cooking spray.
Bake for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F in the thickest part of the chicken.
Let the chicken rest for 5 minutes before serving. Enjoy!