Fill a large pot with salted water and bring it to a boil. Add live lobsters and cook for 8-10 minutes until bright red. Remove and let cool.

Melt butter in a skillet over medium heat. Add shallots and sauté for 2 minutes. Add sliced mushrooms and cook for 4-5 minutes.

Deglaze the skillet with white wine, simmer for 3-4 minutes. Stir in heavy cream and cook for another 3 minutes.

Chop lobster meat and fold into warm sauce with paprika and half of the Parmesan. Season with salt and pepper to taste.

Preheat broiler to high. Fill lobster shells with the mixture and top with remaining Parmesan. Broil for 3-5 minutes until bubbly and golden.

Let cool slightly before serving with salad or crusty bread.