1. To prepare stock, preheat oven to 425°. Spread chicken wings and next 3 ingredients (through onion wedges) in a single layer on a large baking sheet; bake at 425° for 40 minutes or until golden. Scrape chicken wing mixture and pan drippings into a large Dutch oven. Add 3 quarts cold water and next 3 ingredients (through bay leaf); bring to a boil over medium heat. Reduce heat to low, and simmer very gently for 2 1/2 hours, skimming surface as necessary. Strain mixture through a fine-mesh sieve lined with a double layer of cheesecloth over a bowl; discard solids. Wipe pan with paper towels. Return stock to pan; bring to a boil. Cook until reduced to 6 cups.
2. To prepare soup, combine club soda, oil, and eggs in a medium bowl, stirring well. Stir in matzo meal, dill, 1/4 teaspoon salt, and 1/4 teaspoon ground pepper; chill 30 minutes. Shape dough into 24 (1/2-inch) balls.
3. Combine reduced stock and chicken leg quarters in a large Dutch oven over medium-high heat; bring to a simmer. Reduce heat, and cook 30 minutes or until chicken is done, skimming surface as necessary. Remove chicken from pan; cool slightly. Shred chicken with 2 forks; discard bones. Add matzo balls, 1 cup sliced carrot, and 1 cup sliced celery to stock in pan; bring to a simmer. Cook for 20 minutes. Stir in vertically sliced onion; cook 5 minutes or until matzo balls are thoroughly cooked. Remove from heat; stir in shredded chicken, remaining 3/4 teaspoon salt, remaining 1/4 teaspoon pepper, 2 tablespoons parsley, and chives.
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