1. Sprinkle chicken with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Combine the 1/2 cup flour, 1/2 teaspoon poultry seasoning and the chicken in a resealable plastic storage bag; seal bag and shake to coat.
2. Heat oil in a Dutch oven over medium-high heat. Add half the chicken; reduce heat to medium and cook until well browned. Set aside. Repeat with remaining chicken. Discard drippings. Cook leeks and onion 5 minutes, until softened. Add enough water to broth to equal 2-1/2 cups; pour into Dutch oven. Add chicken, carrots, celery, remaining 1/2 teaspoon salt, 1/2 teaspoon poultry seasoning and 1/4 teaspoon pepper. Bring to a boil; reduce heat and simmer, covered, 30 minutes, until chicken is tender. Stir in peas.
3. For dumplings, combine the 1-1/2 cups flour, the parsley, baking powder and 1/2 teaspoon salt in a medium bowl. Add half-and-half cream and stir until dough is moistened. Drop 8 heaping tablespoons of dough into Dutch oven. Cover and simmer 12 minutes, until a toothpick inserted in dumpling comes out clean. Makes 4 servings.