In a large saucepan or stockpot, combine the 1 cup chopped onions, bay leaf, parsley, salt, and water. Cover and bring to a boil over high heat. Add the fish. Reduce the heat and simmer, uncovered, for about 6 minutes, or until the fish is firm to the touch. Remove the fish and cut into 1-inch chunks. Strain the broth through a fine sieve, pressing down on the onions to extract all the juice. Set aside.

Wipe out the saucepan and melt the butter in the pan. Add the 1 to 2 cups chopped onions and saute until the onions are soft but not brown, about 5 minutes. Then add the cucumbers and tomatoes and simmer for about 10 minutes. Add the reserved fish broth and 1 quart clam broth or other fish broth, along with the remaining ingredients. Simmer for about 15 minutes. Then add the fish and continue simmering until the fish is warmed through. Serve hot or warm.