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.

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.