Preheat oven to 400 degrees. Lightly oil a rack large enough to hold chicken breasts in a single layer. Put the rack on a baking sheet and set aside.
Place chicken breasts in a ziploc bag. With a meat pounder, pound the breasts until they are flattened to approximately ΒΌ inch.
Place 1 slice of Swiss cheese and 1 slice of ham on each breast. Roll up starting with the smaller end.
Combine egg whites, buttermilk and mustard and beat with a whisk until creamy.
In a shallow dish, stir together bread crumbs, parmesan, salt and pepper.
Dip each breast in the crumb mixture. Set on the prepared rack and bake for 30-35 minutes, until crisp and lightly browned on the outside.
Dip each chicken breast in a mixture of parmesan cheese, salt and pepper, then a beaten egg, then back in the parmesan cheese mixture.