Season chicken with 1/8 teaspoon each salt and pepper. Mix flour with 1/2 teaspoon salt and 1/4 teaspoon pepper. Sprinkle chicken with 1 tablespoon of seasoned flour. In a large skillet, heat oil and lightly brown chicken. Remove from pan.
In the same skillet, sauté leeks and shallots until lightly golden, about 3 minutes. Add carrots, celery, bay leaf and thyme and cook another 3 minutes. Stir in remaining tablespoon of seasoned flour and it cook until it begins to color, about 1 minute. Pour in chicken broth and apple juice. Return chicken to pot. Bring to boil; reduce heat and simmer, partially covered, until chicken is cooked through, 5 to 7 minutes.
Meanwhile to make dumplings, sift 2 tablespoons flour, cornmeal, baking powder and 1/4 teaspoon salt together into a bowl. Stir in parsley. With a fork, stir in milk until dough just comes together. Drop dumpling mixture with a teaspoon into chicken mixture.
Simmer, covered, about 6 to 8 minutes.
Add peas, and cook until dumplings are done, another 2 to 4 minutes. Serve in six 1-cup portions.