1. Cook the Lobsters

• Fill a large pot with salted water and bring it to a boil. Submerge the lobsters and cook for 8–10 minutes until the shells turn bright red. Remove the lobsters and place them in an ice bath to stop the cooking process.

2. Prepare the Lobster Meat

• Once the lobsters are cool enough to handle, split them in half lengthwise using a sharp knife. Remove the meat from the claws, tail, and body, and chop it into bite-sized pieces. Keep the shells intact, as they will be used for serving.

3. Sauté the Lobster Meat

• Heat olive oil and 1 tablespoon of butter in a skillet over medium heat. Add the chopped lobster meat and sauté for 1–2 minutes until lightly golden. Remove from the skillet and set aside.

4. Make the Sauce Base

• In the same skillet, melt the remaining tablespoon of butter and sauté the chopped shallot until soft and translucent. Add the white wine and simmer for 3–4 minutes to reduce by half. Stir in the heavy cream, mustard, paprika, and cayenne pepper. Let the sauce simmer gently for 5–7 minutes until slightly thickened.

5. Enrich the Sauce

• Remove the skillet from heat and whisk in the beaten egg yolks and grated Gruyère cheese. Stir until the sauce is smooth and creamy. Add lemon juice and season with salt and black pepper to taste.

6. Combine and Fill

• Mix the sautéed lobster meat into the sauce, ensuring it is evenly coated. Spoon the mixture back into the empty lobster shells, filling them generously.

7. Broil the Lobsters

• Preheat your broiler to high. Place the filled lobster shells on a baking sheet and sprinkle with additional Gruyère cheese. Broil for 3–5 minutes, or until the cheese is bubbly and golden.

8. Garnish and Serve

• Remove from the broiler and garnish with fresh parsley if desired. Serve immediately with a side of crusty bread or a light salad.