Prepare the kneidel mix according to package directions, using the eggs and oil.
Add ground chicken, matzah meal, and pepper and mix well to combine.
In a food processor, using the kugel blade, grate the potato and onion.
Squeeze out the liquid and add to the kneidel mixture; mix well to combine.
Divide the mixture into two bowls.
Process herbs using the S-blade and add to one of the bowls.
Grate zucchini and squeeze out liquid; add to the bowl with herbs. Mix well to combine; refrigerate.
Grate carrot and add to second bowl, mix well to combine and refrigerate.
While mixtures are chilling, bring a large pot of water to a boil; add one tablespoon salt.
Working with wet hands, form ping-pong-sized balls of kneidel mixture and drop into pot.
Simmer kneidlach for about 30 minutes, making sure all sides have a chance to be immersed in the water.
Remove from pot to drain.
Serve one of each color kneidel with a portion of soup.
