To purge live crawfish:

Put the crawfish in a large container filled with salted water. Let sit for 30 minutes. Drain and rinse in cold running water until the water runs clear.

To make the crawfish stock:

Combine the 3 quarts of water, salt, crab and shrimp boil, onions, celery, lemons, bay leaves, and peppercorns in a heavy 8-quart stockpot. Bring to a boil and cook for 5 minutes. Add the purged crawfish in a basket and cook until they turn bright red, 10 to 12 minutes. Transfer the crawfish to a baking sheet and spread evenly to cool. When cool enough to handle, peel the crawfish, reserving the tails and discarding the shells. Strain the cooking liquid through a fine mesh strainer into a clean container. (Alternately, if live crawfish are not available, add 1 pound of shrimp shells to the boiling liquid. Boil for 30 minutes to make a rich shrimp stock. Strain the cooking liquid and discard the shells.)

Trim the leeks, discarding the green tops. Cut the white parts crosswise into 1/2-inch slices and put them in a bowl of ice water to soak for 5 minutes. Drain, then place in a fresh bowl of ice water and soak again for 5 minutes. Drain well.

Melt the butter in a Dutch oven or large, heavy pot over medium-high heat. Add the leeks and cook, stirring, until soft, about 5 minutes. Add 1 quart of the strained stock and the potatoes. Reduce the heat to medium-low and simmer, stirring occasionally, until the potatoes are soft, about 25 minutes.

Remove from the heat and puree the mixture until smooth with a hand-held immersion blender, or in batches in a food processor or blender. Adjust the seasoning, to taste.

Scald the cream in a small saucepan over medium-high heat. Remove from the heat and add to the pureed soup, stirring well with a large wooden spoon. Chill the soup completely before serving.

For the Lemon Poached Leeks:

Trim the leeks, discarding the green tops. Cut into thin strips and place in a bowl of ice water. Soak for 5 minutes to remove any grit, then drain. Place in a clean bowl of ice water and soak again for 5 minutes. Drain well.

Combine the crawfish stock, wine, lemon peel, bay leaves, and pepper in a medium saucepan. Bring to a boil. Reduce the heat to medium-low. Add the leeks and simmer until tender, about 10 minutes. Remove from the heat and let the leeks sit in the poaching liquid for 10 to 15 minutes.

Drain in a fine mesh strainer. Discard the bay leaves and reserve the poaching liquid as desired for another use. Set the leeks aside until ready to serve.

For the French Bread Croutons:

Preheat the oven to 400 degrees F.

Place the bread on a baking sheet and brush 1 side of each slice with the olive oil, then lightly season with the salt and pepper. Bake for 8 minutes, or until light golden brown. Remove from the oven and let cool slightly.

Serve the croutons to accompany dips or soups.

To serve, ladle the soup into bowls and arrange 8 to 12 chilled, cooked crawfish tails around the edge of the soup. (Alternately, if using frozen tails with shrimp stock, see directions in the headnote, above.) Place 1 heaping tablespoon of the Lemon Poached Leeks in the center of the bowl, and serve with the croutons.