Place the top oven rack in the center position and preheat the oven to 350ºF. Line a large, rimmed baking sheet with parchment paper or a Silpat™ baking mat. Set aside.
Place chicken breasts between two sheets of plastic wrap and pound with a meat mallet or rolling pin until ¼” thick. Top each chicken breast with 2 slices of deli ham and 2 slices of Swiss cheese.
Tightly jelly roll each chicken breast and secure it with toothpicks. Season with salt and black pepper, as desired, and set aside.
Add the flour, ½ tablespoon Italian seasoning, and garlic powder to a shallow bowl. Season with salt and black pepper, to taste, and stir to combine. Set aside.
Add the eggs and water to a second bowl. Whisk to combine and set aside.
Add the breadcrumbs, Parmesan cheese, and remaining Italian seasoning to a third bowl. Lightly season with additional salt and black pepper, if desired, and stir to combine. Set aside.
Dredge each chicken breast in the seasoned flour until covered on all sides. Then dip the floured breasts into the egg wash and roll until coated. Finally, roll the egg-covered breasts in the seasoned breadcrumb mixture until thoroughly coated.
Transfer each breast to the prepared baking sheet and place it in the preheated oven. Bake for 30-35 minutes or until the chicken reaches a safe internal temperature of just below 165°F on an instant-read thermometer.
Remove chicken from oven and let cool for several minutes before slicing.