Combine the flour, salt, and pepper. Dredge the chicken in the seasoned flour.
In a large pot, heat some olive oil over medium high heat and sear the chicken in batches to avoid overcrowding the pan. When all the chicken is seared return it to the pot.
Heat some olive oil in a skillet over medium-high heat, and saute the leeks, shallots, carrots, and celery adding more oil as necessary. Add the sauteed vegetables, bay leaf, thyme, cider, chicken stock, and salt to the pot with the chicken. Bring to a boil, reduce the heat, cover and simmer for 10 to 15 minutes. Arrange the dumplings into 12 portions on top of the chicken in the pot. Cover and simmer for 12 minutes until the dumplings are plump and fully cooked.
Discard the bay leaf. Serve the stewed chicken with dumplings and juices from the pot.
Preheat the oven to 350 degrees F.
Place the chicken bones on a baking sheet and roast for 40 minutes.
In a large stockpot place the roasted chicken bones and water. Over high heat bring to a boil. Skim the fat and foam from the surface of the water. Add the vegetables, herbs, peppercorns, and garlic. Reduce the heat to medium low and gently simmer for 4 hours. Strain the stock through a fine mesh strainer. Store in the refrigerator for 5 days or freeze.
Sift together the flour, cornmeal, dill, if using, baking powder, mustard, and salt. Add the cream and mix until the dough just comes together.