Grind salmon, red snapper, black cod, ling cod, 2 ½ onions, and 4 carrots together. Place mixture into a large wooden bowl.

Using a hand chopper, add eggs one at a time, mixing well after each addition.

Add sugar, salt, white pepper, and ice water periodically while chopping until mixture is well blended and thick enough to form balls (add more matzo meal if needed).

Fill 2 large stockpots half full of water. Add a sliced onion, slice of carrot, fish skins (optional), sugar, paprika, black pepper, and additional salt if needed. Boil for 10 minutes.

Shape fish mixture into oval balls using wet hands and drop gently into boiling stock.

Cover stockpots slightly and cook over medium-low heat for 2 hours.