1. Place the fish parts, salt, onions, carrots, sugar, and water in a large stockpot and bring to a boil. Reduce the heat to maintain a simmer, cover, and simmer for at least 45 minutes before poaching the quenelles. Skim off any foam that rises to the surface.
2. Wet your hands and form the gefilte fish mixture into about 10 quenelles the size of an egg, with a similarly oblong shape. They will expand as they cook.
3. Place them one by one into the poaching liquid. When all the servings are in the pot, make sure the heat is on low and cover the pot. Poach for
30 minutes. Remove the quenelles with a slotted spoon and place them in a bowl or deep serving dish. Spoon enough poaching liquid over to cover the quenelles and let cool slightly before refrigerating. The poaching liquid will gel slightly as it chills.
4. To serve, remove the carrots and cut them into 3-inch-thick rounds. Serve the quenelles chilled, with the carrot pieces and fresh horseradish relish. If you’re old-school or adventurous, serve with spoonfuls of the poaching gel alongside.
Note If poaching, a fishmonger can save the head, bones, and tail for you if he/ she sells you the fillet—just ask. The poaching liquid can be made without these fish parts, but the gefilte quenelles will be slightly less flavorful.