Preheat oven to 350 degrees F. Lightly grease a 9×13-inch baking dish with cooking spray. Set aside.
In a medium bowl, combine the breadcrumbs and melted butter. Set aside.
Lay the 6 chicken breast cutlets in a single layer in the baking dish. Top each chicken breast with two slices of ham, overlapping so they cover the entire breast. Lay two slices of Swiss cheese overlapping to cover the ham. Repeat with all chicken breasts, ham slices, and Swiss cheese. Sprinkle the breadcrumbs evenly over the tops of all the chicken.
Bake uncovered for 30 to 35 minutes, or until the chicken is cooked through, cheese is bubbling, and breadcrumbs are golden brown.