1. Wash chicken pieces; pat dry. Place in a single layer in a large shallow dish; pour 1 cup of the cream over top; chill at least 20 minutes.
2. Shake chicken pieces, a few at a time, in a mixture of the 2 cups flour, 2 teaspoons salt and 1/4 teaspoon pepper in a paper bag to coat well. Dip each again in remaining cream in dish; shake again in flour mixture.
3. Melt enough shortening or pour enough vegetable oil into each of two large heavy frying pans to make a depth of 1 1/2 inches; heat. Add chicken pieces, skin side down. Brown slowly, turning once, then continue cooking 30 minutes, or until tender. Remove; keep warm while making gravy.
4. Pour all drippings from frying pans into a small bowl; measure 2 tablespoonfuls and return to one pan. Stir in 1 tablespoon of flour, remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring constantly, until bubbly. Stir in remaining 2 cups cream; continue cooking and stirring, until gravy thickens and boils 1 minute.