Preheat the oven to 350. Spray a 9 x 9 baking dish with cooking spray. Mix the bread crumbs together on a plate or flat dish.
To make each chicken roll up, layer one slice of ham and one slice of Swiss cheese on each of the chicken pieces. Roll up tightly, then roll in the bread crumb mixture. Secure with toothpicks (I used two per piece) and place in the prepared baking dish.
Spray with cooking spray. Bake 30 - 35 minutes, or until cooked through.
When the chicken has about 15 minutes left, make the sauce.
Melt the butter in a saucepan over medium heat. Add the flour and whisk to form a smooth paste. Cook 2-3 minutes, until golden. Add the milk, whisking constantly, until combined. Cook until slightly thickened, then slowly add the chicken broth while continuing to whisk constantly to prevent lumps. Whisk in the salt and pepper.
When the sauce has thickened, remove from heat and whisk in the dijon mustard and parmesan cheese until melted and combined. Serve chicken over pasta or rice and drizzle with sauce.