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

Melt butter in a skillet over medium heat. Sauté chopped shallots until translucent, about 3-4 minutes. Add sliced mushrooms and cook until tender, an additional 4-5 minutes.

Pour in white wine and scrape up bits from the skillet. Let simmer for 3-4 minutes to reduce. Stir in heavy cream and cook until the sauce thickens, about 3 minutes.

Fold in chopped lobster meat, paprika, and half of the grated Parmesan cheese. Mix well and season with salt and pepper to taste.

Spoon lobster mixture into cleaned shells and top with remaining Parmesan cheese. Preheat the broiler on high, place shells on a baking sheet, and broil for 3-5 minutes until golden brown.

Remove from oven and let cool slightly. Serve hot, ideally alongside a crisp salad or crusty bread.