Butterfly each chicken breast by slicing horizontally through the middle of the breast, taking care to not cut all the way through. Open the chicken breast up like a book.
Lay the breast flat between 2 pieces of plastic wrap. Use a meat mallet or rolling pin to pound the chicken breasts into a thin, even layer.
Sprinkle the chicken breasts with salt and pepper. Place a slice of ham and slice of Swiss cheese on each chicken breast.
Gently roll up the chicken breast.
In a shallow bowl, combine the breadcrumbs, Italian seasoning, onion powder, garlic, powder, salt, and pepper. Set up a breading station with 2 shallow bowls; one of melted butter and one for the breading.
Dip the chicken rolls in the melted butter, and roll in the breadcrumbs until completely coated. Transfer to a parchment linked baking sheet.
Bake the chicken for 35-40 minutes or until it reaches an internal temperature of 165°F.
To make the sauce, melt the butter in a saucepan over medium heat. Stir in the flour. Then, slowly pour in the milk while whisking to incorporate.
Add in the Dijon mustard and Worcestershire sauce. Season with salt. Spoon the sauce over the chicken.