Pat the chicken dry with paper towels. Use a sharp knife to cut each chicken breast in half horizontally to create two chicken breast halves. Place the chicken breast halves between two sheets of plastic wrap and use a meat mallet or rolling pin to pound them into thin and evenly (be careful not to pound so hard that the meat tears.).

Top each piece of chicken with a slice of ham and a handful of shredded cheese. Roll tightly, tucking the sides a little, and place on a new piece of plastic wrap.

Wrap the chicken tightly in the plastic wrap, pinching the excess plastic on the sides to create a tootsie-roll shape and twisting them to create a firm chicken roll. Refrigerate the wrapped chicken bundles for at least 30-minutes or up to one day in advance.

Preheat oven to 400 degrees F. Remove chicken from fridge, unwrap and season with salt and pepper. Add cornflakes to a food processor and pulse into fine crumbs. Add crumbs to a shallow dish or pie plate. Melt butter in a separate shallow dish.

Dip the chicken bundles in melted butter, and then into the cornflake crumbs, pressing lightly to help the crumbs stick to the chicken. Transfer to a lightly greased baking sheet.

Bake on the center oven rack for about 30 minutes, or until chicken is cooked through (160 degrees on a thermometer inserted into the chicken, not the filling.)

Make the sauce by stirring the mayo and mustard together. Taste and add more mustard, as needed, to taste.