Pat chicken dry with paper towel. Trim fat from chicken breasts. With a sharp knife, cut chicken breasts horizontally into 2 to 3 slices. 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.
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 1/2 cups, about 20 minutes. Yield: 1 1/2 cups.