Mix the eggs, butter or fat, salt, and club soda together for the matzo meal. Add the matzo meal and stir just until combined. Cover and place it into the refrigerator for 1 - 2 hours or until firm.
Place the chicken in a dutch oven and add enough water to cover the chicken by 1-2 inches.
Cover and bring to a boil over high heat. Skim off any of the foam and fat on the surface.
Add the chopped vegetables and simmer until tender. Remove the cooked chicken from the broth and shred the meat if you would like chicken in your soup.
Bring a pot of salted water to a boil for the matzo balls. To form the balls, lightly wet your hands and roll the mixture into walnut size pieces.
Drop the balls into the boiling water and bring it down to a simmer. Simmer for 25-30 minutes, covered.
To serve, drain the matzo balls with a slotted spoon. Ladle the chicken broth over the matzo balls and garnish with fresh dill.
OPTIONAL: I added the vermicelli noodles to mimic Ivy's hair but you can leave it out or substitute another type of pasta.