1. In a 3- to 4-quart enameled or stainless-steel casserole, combine 2 quarts of water with the onions, bay leaf, peppercorns, parsley, salt, pepper and fish trimmings. Bring to a boil over high heat, then reduce the heat to low and partially cover the casserole. Simmer undisturbed for 30 minutes.
2. Strain the stock through a fine sieve set over a large bowl. Press down hard on the vegetables and trimmings with the back of a large spoon to extract all their juices before discarding them. Return the stock to the casserole.
3. In a small bowl, beat the egg whites to froth, add them to the stock, and bring the mixture to a boil over high heat, stirring constantly with a whisk. When the stock begins to froth and threatens to overflow the pan, remove it from the heat and let it rest about 5 minutes.
4. Then slowly pour the entire contents of the pan into a cheesecloth lined sieve set over a deep bowl. Let the stock drain through the sieve without disturbing it at any point. Discard the contents of the sieve and taste the stock for seasoning. It will doubt-less need more salt.
FISH:
1. Return the stock to the casserole and bring it to a boil over high heat. Drop in the fish fillets, reduce the heat to low, and simmer the fish un-covered for 3 to 4 minutes, or until it is firm to the touch and opaque. Do not overcook.
2. With a slotted spoon, remove the fish from the casserole to a platter and cut it into 2-inch slices. Pour the soup into a heated tureen or individual soup bowls. Add the slices of the fish and lime, and sprinkle with the cut dill or chopped parsley.
