Place once slice ham, one slice Swiss cheese, and three asparagus spears in middle of each piece of chicken. Roll up and secure with a toothpick. (I soak my toothpicks in water to prevent them burning in the oven).
Beat egg and evaporated milk together. Dip chicken in egg mixture and then roll in bread crumbs. Salt and pepper chicken to taste.
Arrange in a heavily buttered dish. Bake covered in a 350 degree F oven for 1 hour and 15 minutes.
To make sauce, first remove toothpicks and transfer cooked chicken to warm serving platter. Deglaze the baking dish with white wine, making sure to scrape out all browned bits from baking dish.
Pour deglazing liquid from baking dish into a small stove top saucepan on low heat. Add chicken stock (and butter, if you wish) to deglazing liquid and simmer for 30 minutes.
Blend cornstarch with cream and whisk slowly into skillet.
Cook, stirring until thickened, and pour over chicken. Serve immediately.