Pat chicken dry with paper towel. Trim fat from chicken breasts. With a sharp knife, cut chicken breasts horizontally into 2 to 3 slices. If necessary, pound chicken slices to about ¼-inch thick. Set aside.

Whisk egg and milk in a wide shallow bowl; set aside. Combine flour, salt and pepper in a gallon Ziploc bag. Pour bread crumbs onto a dinner-size plate or piece of waxed paper. Set aside.

Dredge chicken in flour mixture; dip in egg mixture, allowing excess to drip off. Dredge chicken again in flour mixture. Dip chicken in egg mixture, allowing excess to drip off; coat with bread crumbs, pressing bread crumbs onto chicken. Place in single layers on waxed paper; refrigerate for at least one hour.

Heat vegetable oil in a large over medium heat. Add several pieces of chicken; cook until golden brown on both sides, 5 to 6 minutes each side. Transfer to plate lined with paper towels and place in 200°F oven to keep warm. Repeat with remaining chicken. Serve Chicken Schnitzel with Mustard Cream Sauce.

Melt butter in a medium saucepan over medium heat. Add the flour and cook, stirring, for 2 minutes. Whisk in the mustard and pepper and continue to cook for 1 minute. Slowly whisk in the chicken broth and heavy cream. Bring mixture to a boil, whisking constantly. Reduce the heat to medium-low and simmer until the sauce is thickened and reduced to about 1 ½ cups, about 20 minutes.