### Prepare the Lobsters: Bring a large pot of salted water to a rolling boil. Carefully plunge the live lobsters headfirst into the boiling water. Cover the pot and cook for 8-10 minutes, or until the shells are bright red. Remove the lobsters from the pot and plunge them into an ice bath to stop the cooking process. This also makes them easier to handle. Once cool enough to handle, carefully twist off the claws and crack them to extract the meat. Set the claw meat aside. Separate the tail from the body. Using kitchen shears, cut along the underside of the tail to remove the meat in one piece. Slice the tail meat into bite-sized medallions. Clean out the lobster head cavity, discarding any tomalley (green stuff) or stomach sac. Rinse the cleaned half shells and set aside.

### Sauté the Shallots: In a medium saucepan, melt 1 tablespoon of unsalted butter over medium heat. Add the finely diced shallots and cook until softened and translucent, about 3-5 minutes, being careful not to brown them.

### Deglaze with Wine: Pour in the dry white wine, bringing it to a simmer. Let it cook for 2-3 minutes, allowing most of the alcohol to evaporate and the flavors to concentrate.

### Create the Cream Sauce: Reduce the heat to low. Whisk in the heavy cream and whole milk. Bring the mixture to a gentle simmer, then remove from heat. In a small bowl, whisk the egg yolks with a tablespoon of the warm cream mixture to temper them. Gradually whisk the tempered egg yolks back into the cream sauce in the saucepan. Return the saucepan to very low heat, stirring constantly, until the sauce thickens slightly. Do not boil, or the eggs may scramble.

### Flavor the Sauce: Stir in the Dijon mustard, Worcestershire sauce, and fresh lemon juice. Add the remaining 1 tablespoon of unsalted butter and stir until melted and incorporated. Season the sauce with salt, freshly ground black pepper, and a pinch of cayenne pepper (if using) to taste.

### Combine Lobster and Sauce: Gently fold the cooked lobster meat (both tail and claw) into the cream sauce. Ensure all the lobster pieces are well coated.

### Assemble and Bake: Preheat your broiler to high. Arrange the cleaned lobster half shells on a baking sheet. Spoon the lobster and sauce mixture généraously back into the empty shells, mounding it slightly. Sprinkle the top of each filled shell with grated Gruyere cheese. Place the baking sheet under the preheated broiler for 3-5 minutes, or until the cheese is melted, bubbly, and beautifully golden brown. Watch carefully to prevent burning.

### Garnish and Serve: Carefully remove the baking sheet from the broiler. Garnish the Decadent Lobster Thermidor Recipe with fresh chopped parsley. Serve immediately with your favorite side dishes, such as crusty bread, rice pilaf, or a simple green salad.