Ingredients

• 4 ounces cremini mushrooms
• 1 medium shallot
• 1 large clove garlic
• 4 sprigs fresh parsley
• 1 sprig fresh tarragon (optional)
• 1 small lemon
• 2 ounces Gruyère cheese
• 2 (about 1 pound) whole cooked lobsters, thawed if frozen
• 1/2 cup heavy cream
• 2 large egg yolks
• 1/4 teaspoon kosher salt, plus more as needed
• 2 tablespoons unsalted butter
• 1/4 cup Cognac
• 1 tablespoon all-purpose flour
• 1/2 teaspoon Dijon mustard
• 1/4 teaspoon cayenne pepper

1. Thinly slice 4 ounces cremini mushrooms (about 1 3/4 cups). Finely chop 1 medium shallot (about 1/4 cup). Mince 1 large garlic clove (about 1 teaspoon). Pick the leaves from 4 freshly sprigs and finely chop until you have 1 tablespoon plus 1 teaspoon. Pick the leaves from 1 fresh tarragon sprig and finely chop until you have 1/4 teaspoon. Cut 1 small lemon into wedges. Grate 2 ounces Gruyère cheese on the large holes of a boxed grater (about 1/2 cup).
2. Twist the claws off of 2 (about 1-pound) whole cooked lobsters. Crack the meat from the claws and discard the claw shells. Chop the meat into bite-sized pieces and place in a medium bowl.
3. Halve each lobster lengthwise through the tail: Start at the tail end with kitchen shears. When you reach the head, use a chef’s knife to cut straight down. Remove the meat from the tail, reserving the shells. Cut the meat into bite-sized pieces and add to the bowl of claw meat. Refrigerate until ready to use.
4. Remove the gills and other parts inside the top half of the lobster so you are left empty shells. Rinse the shells and pat dry with paper towels. Place cut-side up on a rimmed baking sheet (line with aluminum foil first if desired), spacing them evenly apart.
5. Arrange a rack in the upper third of the oven and heat the oven to broil. Place 1/2 cup heavy cream, 2 large egg yolks, and 1/4 teaspoon kosher salt in a medium bowl and whisk to combine.
6. Melt 2 tablespoons unsalted butter in a medium skillet over medium-high heat. Add the mushrooms and sauté until tender and starting to brown, about 3 minutes. Add the shallot and garlic, and cook, stirring occasionally, until the shallot and garlic are tender and fragrant, about 2 minutes.
7. Carefully pour in 1/4 cup Cognac and bring to a boil. Boil until almost evaporated, 1 to 2 minutes. Add 1 tablespoon all-purpose flour and cook, stirring constantly, until the flour is lightly toasted, about 1 minute.
8. Add the egg yolk mixture and bring to a simmer, scraping up the browned bits from the bottom of the pan with a wooden spoon. Reduce the heat to medium and simmer, stirring constantly, until slightly thickened, 1 to 2 minutes. Add the lobster meat, tarragon, 1 tablespoon of the parsley, 1/2 teaspoon Dijon mustard, and 1/4 teaspoon cayenne pepper. Stir to combine. Taste and season with kosher salt as needed.
9. Remove the pan from the heat. Add half of the cheese and stir to combine. Spoon the lobster mixture evenly into the lobster shells (about 1/2 cup each). Sprinkle with the remaining cheese.
10. Broil until the cheese is melted and golden brown, 4 to 5 minutes. Garnish with the remaining 1 teaspoon parsley and serve with the lemon wedges.