Chef John's Creamy Lobster Thermidor

Cut along the sides of lobster tails using kitchen shears, being careful not to remove the shell at this stage.

Melt 2 tablespoons of butter in a skillet over medium-high heat, allowing it to simmer. Place the lobster tails cut side down in the butter and cook for about 3 minutes, covered. Carefully flip them over due to their curved shape; cover and cook for another minute. Flip them again, covering and cooking for 1 minute more.

Transfer the lobster tails to a bowl, removing any shell pieces from the skillet.

Place 1 tablespoon of butter in the same skillet over medium heat, warming it up. Add shallots and a pinch of salt to the pan; cook and stir until the pan starts to deglaze and the shallots soften, taking around 3-4 minutes. Add mushrooms; cook and stir until they're golden brown, approximately 5-6 minutes. Add flour; stir until the mushrooms are coated and cook for an additional 2 minutes.

Pour in cognac; use a kitchen torch to carefully caramelize the alcohol, taking just a few seconds. Add milk; cook and stir until the pan is completely deglazed, the milk begins to thicken, and it starts to bubble, about 2 minutes. Remove from heat. Stir in creme fraiche and let it cool down.

Remove the lobster meat from its shell, leaving the top shell intact. Remove any bits of bottom shell from the meat.

Preheat your oven to 450 degrees F (230 degrees C). Line a baking pan with crinkled up foil, creating 4 channel-like indentations in the foil to hold and stabilize the lobster tails as they bake.

Slice the lobster meat down the middle, checking for and removing any dark veins. Chop it into 1/2-inch pieces. Transfer the meat to a mixing bowl. Add the cooled sauce, tarragon, a pinch of salt, and cayenne pepper; stir gently until well blended.

Divide the mixture among the lobster tail shells; place them in prepared foil-lined pan. Sprinkle each lobster tail with about 1/2 teaspoon of bread crumbs and 1/2 teaspoon of grated cheese. Drizzle melted butter on the stuffed shells.

Bake in the preheated oven until nicely browned and heated through, about 10 minutes. If desired, you can turn on the broiler and broil for an additional minute until the tops are golden and crispy.