Preheat the oven to 400 degrees F. Set up a dredge station. Place the flour in a shallow bowl, beat the egg in another shallow bowl, and pour the panko into a third bowl. Set aside
Place the chicken breasts on a large cutting board and cover them with a piece of plastic wrap to prevent splattering. Use a meat mallet or rolling pin to pound the chicken out until about ¼-inch thick.
Flip the chicken so the underside of the breast is facing up. Place two slices of ham and two slices of Swiss cheese on each breast. Tightly roll the chicken up, starting on the long side of the breast, then secure closed with toothpicks.
Dredge the chicken in the flour, followed by the egg, and then finally the panko so it is completely coated.
Place the chicken seam side down in a small baking dish.
Bake for 25-30 minutes, or until the internal temperature of the chicken reaches 165 degrees F.
Meanwhile, prepare the sauce by melting the butter in a medium saucepan over medium heat. Whisk in the flour and cook for 2-3 minutes, stirring constantly.
Add the dijon and cook for one minute more. Slowly pour in the chicken broth, whisking constantly to avoid lumps. Add the half and half, whisk to combine, and allow the sauce to simmer for 4-5 minutes or until thickened, stirring often.
Remove the chicken from the oven and allow to rest for 5 minutes. Serve with the Dijon sauce poured over top and a sprinkle of chopped parsley for garnish, if desired.
Notes
Nutritional information is for 1 chicken cordon bleu breast and 1/2 of the sauce.