Step 1Pull off the legs of the shrimp, then peel them, saving the shells. Pull off the tail and devein.
Step 2In a large saucepan with a lid, heat the butter and 2 tablespoons of the olive oil over medium heat. Add the fennel and shallots and saute until tender and beginning to caramelize, about 10 minutes. Add the shrimp shells and white wine and continue to cook until the shells have good color and are caramelized, about 10 minutes.
Step 3Add one-half cup of the Pernod, then ignite with a kitchen lighter or long match. After the flames have subsided, add the tomato paste, bay leaves and 2 quarts water. Stir, cover and cook for about 30 minutes.
Step 4Add the rice, cover and cook for another 30 minutes. (If all of the liquid evaporates and the mixture seems dry, add water as necessary.)
Step 5Meanwhile, saute the shrimp in about 2 tablespoons olive oil and a pinch of salt in a large pan over high heat, until just done, about 3 minutes. Set aside.
Step 6When the shell-rice mixture is done (the rice should be mushy, even overcooked), take it off the heat and let it cool briefly. Puree the mixture plus all but 8 of the shrimp in a food processor in batches. (You will be pureeing the shells too.)
Step 7Put a tamis over a large bowl and press the pureed shrimp mixture through it. It's easier if you do this in batches and take your time. You should have about 4 cups of thick puree when you're finished. Discard the shell mixture that remains in the tamis.
Step 8In a medium pot over low heat, whisk the puree and heavy cream, heating slowly. Add one-half cup water, 1 1/2 teaspoons kosher salt, white pepper and 1 teaspoon Pernod. Strain the soup again through the clean tamis and then back into a medium soup pot and warm over low heat.
Step 9Meanwhile, thinly slice the remaining whole shrimp lengthwise and keep warm, reheating if necessary in a small saucepan. When the bisque is hot, test for seasoning and ladle into soup bowls. Divide the sliced shrimp among the bowls, spooning the shrimp into the middle of the bisque, and serve immediately. This makes about 9 1/2 cups of soup.