Soak the live crawfish in cold water for at least 10 minutes, and then thoroughly wash them, a small batch at a time, in a colander set under cold running water.
Combine the water, the 2 cups of coarsely chopped onions, 3 of the parsley sprigs, the bay leaf, thyme and peppercorns in a heavy 8-to 10-quart pot and bring to a boil over high heat. Using tongs drop in the crawfish and boil them briskly, uncovered, for 5 minutes.
With the tongs or a slotted spoon, transfer the crawfish to paper towels to drain. Then boil the liquid remaining in the pot over high heat until it is reduced to about 2 quarts. Strain the stock through a fine sieve lined with a double layer of dampened cheesecloth and set over a saucepan. Reserve 6 cups of the stock, and discard the vegetables and seasonings.
When the crawfish are cool enough to handle, shell them one at a time in the following manner: With your hands, break off the ridged tail, snap it in half lengthwise and lift out the meat in one piece. Set the meat aside, but discard the tail shell. Some or all of the yellow fat, or "butter" from the body of the crawfish may slide out when you break off the tail. If it does, reserve it.
Snap off the large claws and the smaller legs of the crawfish and-if you like-break the claws with a nutcracker and pick out the bits of meat. Discard the claw shells and legs. Cut off the top of the head just behind the eyes and discard. Then scoop the body shell clean with the tip of a finger or thumb and pick out any fat. Set this shell and all the fat aside, and discard the intestinal matter.
Put all of the crawfish meat and fat through the finest blade of a food grinder, or chop it as fine as possible. There should be about 3 cups of the ground meat. Reserve the meat and 48 of the crawfish body shells, which in Louisiana are referred to as crawfish "heads".
To prepare the bisque, bring the reserved 6 cups of crawfish stock to a boil over high heat. Remove the pan from the heat and cover tightly to keep the stock hot.
In a heavy 6- to 8-quart casserole, warm the brown roux over low heat for 2 or 3 minutes, stirring it all the while. Add 2 cups of the finely chopped onions, the celery and 2 tablespoons of the garlic. Stirring frequently, cook over moderate heat for about 5 minutes, or until the vegetables are soft but not brown.
Stir in the tomatoes, tomato paste, the 3 remaining parsley sprigs and 2 teaspoons of the salt. Stirring constantly, pour in the hot stock in a slow, thin stream and bring to a simmer over moderate heat. Immediately reduce the heat to low and simmer, partially covered, for 45 minutes.
Strain the entire contents of the casserole through a fine sieve set over a deep pot, pressing down hard on. the vegetables and seasonings with the back of a large spoon to extract all their juices before discarding the pulp. Then return the crawfish bisque to the casserole.
Meanwhile, prepare the stuffed crawfish "heads" in the following manner: In a heavy l2-inch skillet, melt 6 tablespoons of the butter over moderate heat. When the foam begins to subside, add the bread crumbs and, stirring frequently, fry them until they are crisp and golden brown. With a rubber spatula, scrape the crumbs into a deep bowl and set them aside.
Add the remaining 8 tablespoons of butter to the skillet and melt over moderate heat. Drop in the remaining cup of finely chopped onions, the scallions and the remaining 2 teaspoons of garlic and, stirring frequently, cook for about 5 minutes, or until the vegetables are soft but not brown.
Scrape the contents of the skillet into the bowl of toasted bread crumbs. Add 2 cups of ground crawfish meat, the ¼ cup of chopped parsley, ½ teaspoon of the red pepper and the remaining teaspoon of salt, and mix the stuffing ingredients together gently but thoroughly.
For each stuffed crawfish head, scoop up about 1 tablespoonful of the stuffing and pack it tightly into one of the reserved shells. Immerse each head in the beaten eggs and turn it about in the flour to coat it evenly. As you proceed, set the stuffed heads aside on a platter or wax paper.
Preheat the oven to its lowest setting, then line a large shallow baking dish with a double thickness of paper towels and set it on the middle shelf of the oven.
Pour vegetable oil into a deep fryer or large heavy saucepan to a depth of 2 to 3 inches and heat the oil until it reaches a temperature of 350° on a deep-frying thermometer.
Deep-fry the coated stuffed crawfish heads, seven or eight at a time, turning them about with a slotted spoon until they are golden brown on all sides. As they are fried, transfer them to the paper-lined dish and keep them warm in the oven until you are ready to serve them.
Shortly before you plan to serve the bisque, bring it to a simmer over moderate heat. Stir in the remaining cup of ground crawfish meat and 1 teaspoon of red pepper and simmer, partially covered, for about 15 minutes. Taste for seasoning. Ladle the bisque into a large heated tureen or individual soup plates and, just before serving, drop in the crawfish heads.