1. Prepare the Lobster:

• Bring a large pot of salted water to a boil. Add the lobsters and cook for about 8-10 minutes, or until they turn bright red and the shells are fully cooked. Remove the lobsters from the pot and set aside to cool for a few minutes.
• Once cool enough to handle, use kitchen shears to cut the lobster shells lengthwise, from the head to the tail. Gently remove the lobster meat from the shell, leaving the shells intact for later use. Cut the lobster meat into bite-sized chunks, discarding the tomalley (green matter) and roe (if present).

2. Make the Sauce:

• In a saucepan, melt 2 tablespoons of butter over medium heat. Add 2 tablespoons of flour, whisking constantly for about 1-2 minutes to form a roux (a thickening paste).
• Slowly pour in 1 cup of heavy cream, followed by 1/2 cup of white wine or cognac, whisking to avoid lumps. Continue to cook, stirring constantly, until the sauce thickens (around 3-4 minutes).
• Stir in the Dijon mustard, paprika, and cayenne pepper (if using), and season with salt and pepper to taste.
• Once the sauce is thickened, remove the saucepan from the heat. In a small bowl, lightly beat 2 egg yolks. Slowly add a few spoonfuls of the hot sauce to the egg yolks, whisking constantly to temper the eggs (this prevents them from curdling).
• Gradually whisk the egg yolk mixture back into the sauce. Return the saucepan to low heat and cook for an additional 2-3 minutes, stirring occasionally until the sauce is smooth and creamy.

3. Assemble the Lobster Thermidor:

• Preheat your broiler to high.
• Return the lobster meat to the lobster shells, packing it in gently. Pour the creamy sauce over the lobster meat in the shells, making sure it’s generously covered. Sprinkle the top with 1/2 cup of grated Gruyère cheese (or Parmesan) for a golden, cheesy crust.

4. Broil:

• Place the lobster shells on a baking sheet and transfer them to the preheated broiler. Broil for 5-7 minutes, or until the cheese is melted, bubbly, and golden brown. Keep a close eye on the lobster, as broilers can vary in heat.

5. Serve:

• Remove the Lobster Thermidor from the oven and let it cool for a few minutes before serving. Garnish with freshly chopped parsley and serve with lemon wedges on the side.