2 whole (about 1 1/2 pounds each) live lobsters
¼ cup unsalted butter
1 medium (2 ounces) shallot, finely chopped (about 1/3 cup)
2 medium garlic cloves, finely chopped (about 1 1/2 teaspoons)
6 ounces cremini mushrooms, thinly sliced (about 2 3/4 cups)
¾ cup heaving whipping cream
2 large egg yolks
2 tablespoons dry sherry
½ teaspoon kosher salt, plus more to taste
¼ teaspoon cayenne pepper
½ cup (3/4 ounce), plus 2 tablespoons finely grated Parmesan cheese, divided
Chopped fresh flat-leaf parsley
Lemon wedges
Bring a large pot (at least 10 quarts) of water to a boil over medium-high. Add lobsters. Cover and cook, adjusting heat as needed to maintain a low simmer. Cook until lobster shells are bright red and you can distinctly smell cooked lobster in the air, 12 to 14 minutes. Transfer lobsters to a rimmed baking sheet until cool enough to handle, about 20 minutes.
Twist off claws, and crack to remove meat. Set meat aside; discard claw shells. Place 1 lobster on a cutting board, and using a large, heavy knife and kitchen shears, cut the lobster in half lengthwise. Carefully remove tail meat. Discard tomalley or reserve for another use. Rinse lobster shells and dry thoroughly. Place shells, cut side up, on a rimmed baking sheet. Repeat with remaining lobster. Chop tail and claw meat into 1/2-inch pieces; set aside.
Heat butter in a large saucepan over medium. Add shallot, and cook, stirring often, until softened, 3 to 4 minutes. Add garlic and mushrooms, and cook, stirring often, until liquid has evaporated and mushrooms begin to brown, 5 to 6 minutes. Meanwhile, whisk together heavy whipping cream, egg yolks, and sherry. Add cream mixture to mushroom mixture, and cook, stirring constantly, until sauce thickens slightly, 1 to 2 minutes. Remove from heat, and stir in salt, cayenne, and 1/2 cup of the Parmesan. Fold in lobster meat, and season to taste with salt. Spoon mushroom mixture evenly into lobster shells (about 1/2 cup each). Reserve any extra filling for a snack if it doesn't fit in the shells. Sprinkle with remaining 2 tablespoons Parmesan.
Preheat broiler with oven rack 6 inches from heating element. Broil until filling is light golden brown, 2 to 3 minutes. Garnish with parsley, and serve with lemon wedges.