Fill a large pot with salted water and bring it to a vigorous boil. Add live lobsters and cover the pot. Cook for 8-10 minutes until the lobsters turn bright red. Remove and cool slightly before cracking open and extracting the meat.

Melt 4 tablespoons of unsalted butter in a large skillet over medium heat. Add finely chopped shallots and stir for about 2 minutes until translucent. Add sliced mushrooms, cooking for another 3-4 minutes until tender.

Pour in ½ cup of dry white wine and simmer for 3-4 minutes until reduced by half. Then add 1 cup of heavy cream, stirring continuously and cooking until the sauce thickens slightly.

Chop the lobster meat into bite-sized pieces and gently fold it into the creamy sauce along with 1 teaspoon of paprika and half of the grated Parmesan cheese. Season with salt and pepper to taste.

Preheat your broiler. Fill the lobster shells with the lobster and sauce mixture and sprinkle the remaining Parmesan cheese over the top. Broil for 3-5 minutes until the cheese is melted and golden brown.

Serve hot on a platter or individual plates. Pair with a Caesar salad or crusty bread.