Bring a large pot of salted water to a boil over high heat. Carefully add the live lobsters, cooking them for 8-10 minutes until bright red. Transfer to an ice bath to cool, then crack them open and chop the meat.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add the chopped shallots and sauté for about 2 minutes until translucent. Add the sliced mushrooms and cook for an additional 5 minutes until tender.

Pour in ½ cup of white wine, scraping the bottom of the skillet to deglaze. Let it simmer for 3-4 minutes until reduced by half. Stir in 1 cup of heavy cream and let it thicken for around 3 minutes.

Fold in the chopped lobster meat, 1 teaspoon of paprika, and half of the grated Parmesan cheese. Mix gently to coat the lobster in the sauce. Season with salt and pepper.

Preheat your broiler to high. Fill the reserved lobster shells with the creamy mixture, packing it in. Sprinkle remaining Parmesan cheese generously on top. Broil for 3-5 minutes until melted and golden brown.

Remove from the oven and let cool slightly before serving. Serve on a platter or individual plates alongside a fresh salad or crusty bread.