Ingredients
Kosher salt
1 1/4 pounds lobster tails in shell (4 small or 2 large)
2 tablespoons extra-virgin olive oil
1 can (15 ounces) fish stock (1 3/4 cups)
1 cup dry white wine, such as Sauvignon Blanc
5 tablespoons unsalted butter
1 head fennel (10 ounces), chopped (2 1/2 cups), plus fronds for serving
1 sweet onion (10 ounces), such as Vidalia, chopped (2 cups)
2 cloves garlic, smashed and peeled
Kosher salt and freshly ground pepper
2 plum tomatoes (8 ounces), cored, seeded, and chopped (1 cup)
1 tablespoon tomato paste
3 sprigs thyme
1 bay leaf
1 teaspoon paprika
1/8 teaspoon cayenne pepper
2 tablespoons brandy or cognac
2 tablespoons dry sherry
1/2 cup heavy cream
1 teaspoon cornstarch
Lemon wedges, for serving (optional)
Preparation
Stock: In a large pot lined with a steamer basket, bring 1 inch salted water to a boil. Steam lobster tails, top-side down, until just cooked through and tails curl under, 6 to 8 minutes for small tails and 8 to 10 minutes for large. Transfer to a plate and let cool. When cool enough to handle, use kitchen shears to cut through underside of tails. Remove meat from shells; reserve shells. Run a paring knife along back of each tail and remove vein. Cut meat into bite-size pieces; cover and refrigerate until ready to use.
Heat oil in a large pot over medium-high. Add shells and cook until fragrant and deep red in color, about 4 minutes. Add fish stock, wine, and 6 cups water; bring to a boil. Reduce heat to medium and simmer, uncovered, skimming impurities from surface, until reduced to 6 cups, 40 to 45 minutes. Strain stock into a large liquid-measuring cup or heatproof bowl. Wipe out pot. (Stock can be stored in airtight containers in the freezer up to 3 months.)
Bisque: In same pot, melt 4 tablespoons butter over medium-high heat. Add fennel, onion, and garlic and season with salt and pepper; cook, stirring occasionally, until soft and translucent, 6 to 8 minutes. Stir in tomatoes, tomato paste, thyme, bay leaf, paprika, and cayenne; cook 1 minute. Add brandy, sherry, and strained lobster stock; season generously with salt and pepper. Bring to a boil, then reduce heat to medium and simmer 30 minutes. Remove thyme and bay leaf.
Working in batches, puree soup in a blender until smooth. Return soup to pot. Let cool 15 minutes. Whisk together cream and cornstarch, then stir into bisque. Bring to a boil and cook, stirring, until thickened slightly, 1 to 2 minutes. Adjust seasoning as desired.
Melt remaining 1 tablespoon butter in a medium saute pan over medium heat. Add lobster meat and cook until just warmed through, 2 to 3 minutes. Pour soup into bowls and serve, topped with lobster, fennel fronds, and a squeeze of lemon, if desired. Soup can be made in advance and stored in an airtight container in refrigerator up to 2 days.
