Fill a large pot with salted water and bring it to a rolling boil. Carefully add the live lobsters and cook for 8-10 minutes until shells turn bright red. Remove and let cool slightly.

Melt 4 tablespoons of butter in a skillet over medium heat. Add 1 cup of finely chopped shallots and sauté for 2 minutes until translucent. Add ½ cup of sliced mushrooms and cook for another 3-4 minutes until tender.

Pour in 1 cup of white wine and let it simmer for 3-4 minutes to reduce by half. Stir in ½ cup of heavy cream, cooking for about 3 minutes until the sauce thickens.

Chop the cooked lobster meat into bite-sized pieces and fold into the mixture. Add 1 teaspoon of paprika and half of the grated Parmesan cheese. Taste and adjust salt and pepper as necessary.

Preheat broiler to high. Spoon the lobster mixture back into cleaned shells and top with remaining Parmesan cheese. Broil for 3-5 minutes until golden brown.

Once bubbling and golden, remove from oven and serve immediately with a crisp salad or crusty bread.