Have your fish market fillet the fish and save the heads and bones for you to make broth. Some will even grind the fish for you, making this an easy job.
Peel and coarsely chop 2 of the onions, and cut the fish into 3-inch pieces. Place half the fish and half the chopped onions in the bowl of a food processor, and process until smooth, about 1 1/2 minutes, scraping the sides of the bowl down 2 to 3 times. Transfer mixture to a large bowl. Repeat process with the remaining onions and fish, and add to the first batch. (If your fishmonger ground the fish, chop onions, process to a coarse puree, and stir into the fish.) To the fish and onions, add salt, sugar, and matzo meal, and mix well with a wooden spoon.
Add eggs and water, and mix to combine. Refrigerate mixture until cold and firm, about 2 hours.
Meanwhile, cut fish bones into 3-inch pieces, and place in a 6 1/2-quart stockpot. Cut remaining onion, 2 carrots, and celery in half, and place in stockpot. Add cloves, 2 dill sprigs, and 1 1/2 quarts water to barely cover bones and vegetables. Bring liquid to a boil, reduce heat, and let simmer for about 35 minutes, skimming off the fat that rises to the surface as necessary.
Remove broth from heat, and strain liquid through a cheesecloth-lined sieve, pressing down on and then discarding solids. Rinse and dry stockpot, and return broth to pot. Set aside.
Remove fish mixture from refrigerator. Wet hands with cold water, and form 2 heaping tablespoons of mixture into an oval shape. Place on a clean plate. Wet hands as necessary and continue until all of the mixture is used up, making 36 to 40 ovals.
Return broth to heat, and bring to a simmer over medium low. Cut 2 carrots into 1/4-inch-thick rounds, and add to the broth. Carefully add fish, cover, and simmer over very low heat until fish is firm and opaque at the center, 20 minutes.
Remove fish from broth with a slotted spoon, and arrange in a single layer in Pyrex baking dishes. Strain broth through a sieve lined with cheesecloth, discarding carrots. Pour strained broth over fish. Cover, and place in refrigerator overnight, allowing the stock to jell.
Prepare an ice-water bath: Fill a large bowl with cold water and ice. Cut remaining carrots into 3-inch matchsticks. Bring a small saucepan of water to a boil, add salt and carrots, and cook until just tender, about 30 seconds. Transfer carrots to ice-water bath for 1 minute. Drain in a colander, transfer to a small bowl, cover, and refrigerate until ready to serve fish.
Remove fish from refrigerator. To serve, arrange 2 pieces of fish and a spoonful of jellied broth on 1 large or 2 small radicchio leaves on each plate. Divide the carrot matchsticks among the plates, and garnish each with a sprig of dill. Pass horseradish on the side.