Combine chicken wings, water, onion, carrot, parsnip, celery, parsley and dill sprigs, and pinch of salt to a large saucepan and bring to a boil. Partly cover and simmer 2 hours, skimming occasionally. Skim off excess fat. (Chicken soup can be kept 3 days in refrigerator or can be frozen; reheat before serving.)
Make matzo balls: In a medium bowl, lightly beat eggs with oil. Add matzo meal, salt and stir until smooth. Stir in water, then let mixture stand for 20 minutes so matzo meal absorbs liquid.
Bring salted water to a boil. With wet hands, roll about 1 teaspoon of matzo ball mixture between your palms into a ball; mixture will be very soft. Set balls on a plate. With a rubber spatula, carefully slide balls into boiling water. Cover and simmer over low heat for about 30 minutes or until firm. Cover and keep warm until ready to serve. (Matzo balls can be kept 2 days in their cooking liquid in a covered container in refrigerator; reheat gently in cooking liquid or in soup.)
To serve soup, remove chicken wings, onion, celery, parsnip, parsley and dill sprigs. Take meat off bones and add to soup; or reserve for other uses. Add pepper to soup, stir in snipped dill and taste soup for seasoning. Slice carrot and add a few slices to each bowl. With a slotted spoon, add a few matzo balls. Serve hot.