1. MAKE THE STOCK: Preheat the oven to 425 degrees. Spread the chicken wings in a large roasting pan and roast for about 30 minutes, until golden brown.
2. Meanwhile, in a large stockpot, heat the vegetable oil. Add the onions, cover and cook over moderately high heat, stirring occasionally, until softened, about 5 minutes. Uncover and cook, stirring frequently, until the onions are lightly browned, about 5 minutes longer. Add the chicken backs, necks and feet, the diced carrots, celery, bay leaves, garlic, thyme, rosemary, peppercorns and 8 quarts of water and bring to a light boil, skimming any scum that rises to the surface.
3. Add the roasted chicken wings to the stockpot. Place the roasting pan over 2 burners, add the vinegar and 2 cups of water and simmer over high heat, scraping up any browned bits. Add the liquid to the pot and simmer gently over moderate heat for 2 1/2 hours. Carefully strain the stock into another large pot and discard the solids, including the wings. You should have about 8 quarts. Let the stock cool, then spoon off all of the chicken fat and reserve it for the matzo balls. Season the chicken stock lightly with salt.
4. MEANWHILE, MAKE THE MATZO BALLS: In a medium bowl, whisk the eggs with the chicken fat, club soda, scallions, rosemary and salt. Whisk in the matzo meal. Refrigerate for 1 hour, until slightly firm.
5. MAKE THE SOUP: Bring a small saucepan of salted water to a boil. Add the sliced carrot and leeks and cook over high heat until tender, about 7 minutes; drain. In a saucepan, bring 2 cups of the stock to a simmer. Add the diced chicken breast and thighs and cook over moderately low heat until just white throughout, about 6 minutes. Transfer the chicken to a plate; reserve the broth for another use (see Note). 6. Bring a large saucepan of the chicken stock to a simmer. Scoop rounded tablespoons of the matzo mixture into balls (about 2 dozen balls) and add them to the simmering stock. Cover and cook over very low heat until the matzo balls are tender, fluffed and cooked through, about 25 minutes. Using a slotted spoon, transfer the matzo balls to a clean pot. Add the chicken, carrots and leeks and 8 cups of the stock and bring to a simmer. Ladle the soup and matzo balls into bowls and serve.