Bring a large pot of salted water to a rolling boil. Add live lobsters and cook for 8-10 minutes until bright red. Remove and cool in ice water, then extract the lobster meat.

Melt 4 tablespoons of unsalted butter in a large skillet over medium heat. Sauté finely chopped shallots until translucent, about 2 minutes. Add sliced mushrooms and cook for an additional 3-4 minutes.

Pour in ½ cup of dry white wine and let simmer for 3-4 minutes until slightly thickened. Slowly stir in 1 cup of heavy cream and cook for another 3 minutes until the sauce begins to thicken.

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

Preheat your broiler to high. Spoon the lobster mixture back into the emptied lobster shells and top with remaining Parmesan cheese. Place on a baking sheet and broil for 3-5 minutes until bubbly and golden.

Remove from broiler, let cool slightly, and serve hot with a light salad or crusty bread.