Dredge chicken in seasoned flour, shaking off excess, and put on a rack.
In a large heavy kettle melt butter with oil over moderately high heat until foam subsides and brown chicken in batches (do not crowd), transferring it to a plate as done, about 5 minutes on each side.
Stir in leeks and shallots and cook 3 minutes, scraping the bottom and stirring occasionally. Stir in carrots, celery, bay leaf and thyme and cook 3 minutes. Stir in broth, cider, and chicken and bring liquid to a boil. Reduce heat and simmer, covered partially, until chicken is cooked through, 10 to 15 minutes.
Make dumplings while chicken is cooking: Into a bowl sift together flour, cornmeal, baking powder, and salt and stir in dill. With a fork stir in half-and-half until dough is just blended.
With a large soup spoon scoop out 12 dumplings and arrange over chicken mixture. Simmer chicken and dumplings, covered, 9 minutes. Sprinkle in peas and cook until dumplings are done, about 3 minutes more. (Dumplngs are done when a wooden pick inserted in center comes out clean.) Discard bay leaf.
Serves: 6