This is Chef John’s recipe. As he says, “Oooooh, it’s so good”!
4 lobster tails (4 oz each)
3 Tbsp butter, divided
2 Tbsp minced shallots
salt to taste
1-1/2 cups diced mushrooms (optional)
1 Tbsp flour
2 Tbsp cognac or brandy
1/2 cup whole milk
2 Tbsp heavy cream
1 Tbsp chopped fresh tarragon or basil
cayenne pepper to taste
2 tsp fine dried bread crumbs
2 tsp finely grated Parmesan cheese
2 Tbsp melted butter
Cut bottom shell of the lobster tail along both sides where it meets with the top shell and discard. Do not remove the top shell at this point.
Melt 2 Tbsp butter in a skillet over medium high heat. Place lobster tails cut side down in the butter. Cook, covered, about 3 minutes. Turn tails over (they are curved, so will lean to one side). Cover and cook one minute. Lean to the other side, cover and cook one minute more.
Remove from heat. Transfer to a bowl. Remove any pieces of shell from the skillet.
Place 1 Tbsp of the butter in the skillet over medium heat. Add shallots and a pinch of salt. Cook and stir until the pan starts to deglaze and the shallots soften, about 3 to 4 minutes. Add mushrooms, cook and stir until they are golden brown, 5 to 6 minutes. Add flour, stir until mushrooms are coated and cook 2 minutes. Pour in brandy, then use a torch to ignite and burn off the alcohol. Add milk, cook and stir until pan is completely deglazed and the milk thickens and bubbles, about 2 minutes. Remove from heat, stir in cream and cool.
Preheat oven to 450 degrees. Line a baking pan with crinkled up foil. Make 4 channel-like indentations in the foil to hold and stabilize the lobster tails as they bake.
Remove lobster meat from the shell, leaving the top shell intact. Remove any bits of meat from the shell.Slice the lobster down the center. Check for and remove any dark veins. Chop the lobster into 1/2 inch pieces; transfer to a bowl. Add the cooled sauce, tarragon, pinch of salt and cayenne pepper. Stir gently until well blended.
Divide the mixture between the four shells; place in foil lined pan. Sprinkle each lobster tail with about 1/2 tsp bread crumbs and 1/2 tsp grated Parmesan cheese. Drizzle with the 2 tsp melted butter.
Bake until nicely browned and heated through, about 10 minutes. If you like, you can turn on the broiler and broil for about 1 minute until the tops are golden and crispy.