Place chicken, onions, garlic, celery, carrots, peppercorns and bay leaves in a large pot and cover with 10–12 cups water.
Season with a good amount of salt and bring to a boil. Reduce heat to medium-low and continue to simmer until the chicken is cooked through and falling apart, about another hour and a half.
Strain the broth and keep it warm or refrigerate overnight.
Combine matzo meal, chives, dill and kosher salt in a medium bowl. Incorporate eggs until well blended. Add chicken fat and club soda, mixing until evenly soaked.
Cover with plastic wrap and refrigerate until mixture is firm, at least 2 hours.
Bring a large pot of well-salted water to a boil. Roll matzo ball mixture into balls and place them on a plate.
Gently plop all of the matzo balls into the boiling water and cook until floating and cooked through, 12 to 15 minutes.
Transfer the matzo balls to the chicken broth to finish cooking.
Add celery and carrots, season with salt, and ladle into bowls. Top with dill, chives, celery leaves, and freshly ground pepper.
