FOR THE STEW: Remove and discard giblets and neck from chicken. Rinse chicken with cold water, and place chicken in an 8-quart stockpot. Add 3 quarts water and next 8 ingredients (through bay leaves); bring to a simmer.
Reduce heat and simmer 45 minutes; skim surface occasionally, discarding solids.
Remove chicken from pot; cool. Strain stock through a sieve into a large and discard solids. Remove chicken meat from bones; tear chicken meat into 2-inch pieces, and store in refrigerator. Let stock cool to room temperature.
Pour stock into zip lock bags. Let stand 15 minutes. Working with one bag at a time, snip off a corner of bag; drain liquid into stockpot stopping before fat layer reaches opening. Discard fat Repeat procedure with remaining bag.
Bring stock to a boil over medium-high heat; reduce heat, and simmer until reduced to about 8 cups (about 15 minutes).
Heat a cast-iron skillet over medium-high heat for 5 minutes. Lightly spoon 1/4 cup flour into a dry measuring cup; level with a knife. Add flour to pan; cook 1 minute or until lightly browned, stirring constantly.
Combine browned flour and cornstarch in a large bowl; add 2/3 cup of the stock to flour mixture, stirring with a whisk until smooth. Add flour mixture to remaining stock in pan; bring to a boil over medium-high heat. Cook 2 minutes or until slightly thickened. Reduce heat; stir in cream. Add chicken; keep warm over low heat.
FOR THE DUMPLINGS: Combine milk and egg in a medium bowl Lightly spoon 1 1/2 cup all-purpose flour into dry measuring cup and level with a knife. Combine the flour, baking powder, cornmeal and 1/2 teaspoons salt.
Add flour mixture to milk mixture, stirring with a fork just until dry ingredients are moistened. Drop one-third of dumpling batter by 8 heaping teaspoonfuls onto chicken mixture. Cover and cook for 3 minutes or until the dumplings are done (do not allow chicken mixture to boil) Remove dumpling with a slotted spoon; place in a large serving bowl or on a deep serving platter; keep warm. Repeat procedure with remaining dumpling batter.
Remove pan from heat; slowly pour stew over dumplings, Sprinkle with chopped parsley and freshly ground black pepper. Serve immediately.