Preheat the oven to 350°F. Use a sharp knife to cut each of the large chicken breasts in half horizontally to create two chicken breast halves. Place between two sheets of plastic wrap and use a meat mallet or rolling pin to gently pound them to approximately ½-inch thickness. If using 4 smaller sized breasts, simply pound them out without slicing them first.
Sprinkle each side of the chicken pieces generously with garlic, salt and pepper. Top each pieces of chicken with sliced cheese, then ham, then more cheese and a tablespoon or two of green chile spread across the cheese. Roll the chicken up and pin each roll with toothpicks.
Mix together the Parmesan and the panko crumbs and sprinkle generously over the chicken. Bake for 35-40 minutes, until the chicken is cooked through. The required time will vary based on the thickness of the chicken.