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

In a skillet, melt butter over medium heat. Add chopped shallots and sauté for about 2 minutes. Add sliced mushrooms, cooking for 3-4 minutes until tender.

Pour in white wine, simmer for 3-4 minutes until reduced by half. Stir in heavy cream and cook for about 3 minutes until the sauce thickens slightly.

Fold the lobster meat into the sauce with paprika and grated Parmesan cheese. Season with salt and pepper.

Transfer the mixture back into the lobster shells. Sprinkle with the remaining Parmesan cheese.

Preheat the broiler to high and broil the filled shells for 3-5 minutes until golden-brown.

Remove from the oven and let cool. Serve hot, ideally with a Caesar salad or crusty bread.