chicken n cornmeal chive dumplings

Name: chicken n cornmeal chive dumplings
Ingredients: for the chicken soup; 1 4 pound chicken; 3 stalks celery, diced; 1 medium onion, diced; 3 carrots, peeled and diced; 1 quart low sodium chicken broth; 2 cups water; 2 teaspoons olive oil; 8 ounces mushrooms, quartered; 1 cup frozen peas; for the dumplings; 1 cup self rising flour or 1 cup all purpose flour +2 teaspoons baking powder; 1/4 cup cornmeal; 1 1/2 teaspoons sugar; 1/2 teaspoon kosher salt; 2 tablespoons finely chopped chives; 1/2 cup half and half; 1/4 cup milk