• Add cornflakes to a food processor and pulse into fine crumbs. Add crumbs to a shallow dish or pie plate. Set aside.
• Melt butter in a separate shallow dish. Set aside. Preheat oven to 400 degrees F.
• Top each ham slice with 2 thin slices of Swiss cheese or a handful of shredded cheese and roll tightly together. Set aside.
• Pat the chicken dry with paper towels. Use a sharp knife to cut a pocket in the thickest part of the chicken breast, following the photos above. Season both sides of the chicken with salt and pepper.
• Place the ham and cheese rolls inside the pocket in the chicken breasts. Secure the edges of the chicken shut with toothpicks.
• Use tongs to gently dip the chicken in melted butter on both sides, and then into the cornflake crumbs, pressing lightly to help the crumbs stick to the chicken. Transfer the chicken to a lightly greased baking sheet.
• Bake on the center oven rack for 25-30 minutes, or until chicken is cooked through (160 degrees on a thermometer inserted into the chicken, not the filling.)
  
• Allow the chicken to rest for 5 minutes before serving.
• Make the sauce by stirring the mayo and mustard together. Taste and add more mustard, as needed, to taste. 

To make ahead:

• The breaded and stuffed (uncooked chicken) can be refrigerated up to 1 day in advance. Bake as directed, but you may need to add a few more minutes to the cook time.