Preheat the oven to 300° F.

Chicken: Wash and dry the chicken pieces with paper towels, lightly salt and pepper the chicken. In a large heavy skillet, melt the butter and brown the chicken pieces over moderate heat until golden brown. Remove to a heatproof platter and reserve in the preheated oven. Add the bones to the skillet and cook, stirring until browned. Add the chopped celery and onions, and cook until they wilt. Add the flour and cook, stirring, for 5 minutes. Add the chicken stock and cream, and reduce the heat to low. Simmer for 30 minutes.

Strain the sauce into a serving tureen, discarding the solids. Fold the dill into the sauce. Add the chicken pieces to the sauce and place in a warm oven.

Dumplings: Sift the dry ingredients into a large mixing bowl. Add the melted butter and buttermilk and blend until smooth. Fold in the chopped dill.

In a large pot, bring the stock to a simmer. Drop the dumpling mixture by soup spoonfuls into the simmering stock. Cover and cook for 5 minutes. With a slotted spoon, turn the dumplings over. Cover and cook 5 more minutes. Continue poaching the dumplings until puffed and cooked in the center. Place the dumplings on top of the chicken and sauce.