In a stockpot, combine the chicken and neck with the water, quartered onion, carrots, celery, garlic, peppercorns, bay leaf, parsley springs, and thyme sprigs and bring to a boil. Cover partially and simmer over low heat for 30 minutes. Transfer the chicken to a plate. Discard the skin. Pull the meat off the bones, cut it into 1/2-inch pieces, and refrigerate.

Return the bones to the pot, partially cover and simmer for 1 hour, until the broth is richly flavored. Strain the broth into a clean heat proof bowl and rinse out the pot. Return the broth to the pot and boil over moderate heat until reduced to 8 cups, about 30 minutes. Season with salt.

In a large saucepan, melt the butter. Add the cabbage, chopped onion, and pickles and cook over moderately high heat, stirring frequently, until just softened, about 10 minutes. Stir in the tomato paste and paprika and cook for 1 minute. Add the broth and bring to a boil. Season with salt and pepper and simmer over moderate heat until the vegetables are very soft, about 20 minutes. Add the chicken, pickle juice, and dill and simmer until just heated through.