Bring a large pot of salted water to a boil over high heat. Add live lobsters and cook for 8 to 10 minutes until they turn vibrant red. Remove, cool slightly, crack open shells, and set lobster meat aside.

In a large skillet, melt 2 tablespoons of unsalted butter over medium heat. Sauté finely chopped shallots for about 3 minutes until translucent. Add sliced mushrooms and cook for 5 minutes until tender.

Pour in ½ cup of white wine and bring to a simmer, reducing by half (about 3 to 4 minutes). Stir in 1 cup of heavy cream and cook for another 3 minutes until the sauce thickens slightly.

Chop reserved lobster meat into bite-sized pieces and fold it into the creamy mixture. Add 1 teaspoon of paprika, salt, and pepper to taste, then mix in half of the grated Parmesan cheese.

Preheat the broiler on high. Spoon the lobster and sauce mixture into cleaned lobster shells, packing it in. Sprinkle remaining Parmesan cheese on top and broil for about 3 to 5 minutes until cheese is golden brown.

Let the shells rest for a minute before serving. Pair with a crisp salad or crusty bread to enjoy this gourmet seafood masterpiece.