Bring a large pot of salted water to a boil. Carefully add the lobsters and cook for 8–10 minutes until bright red. Transfer to ice water to cool, then crack open shells and remove meat.

In a skillet, melt 2 tablespoons of butter over medium heat. Add shallots and sauté until translucent, about 3–4 minutes. Incorporate mushrooms and cook until softened, about 3–5 minutes.

Pour in white wine and simmer, reducing by half, around 5–7 minutes. Stir in heavy cream and cook for an additional 3–4 minutes until thickened.

Chop lobster meat into bite-sized pieces and fold into the creamy sauce. Add paprika and half the Parmesan cheese. Season with salt and pepper to taste.

Transfer the lobster mixture into cleaned lobster shells and top with remaining Parmesan cheese.

Preheat the broiler. Place shells on a baking sheet and broil for 3–5 minutes until golden brown.

Remove from oven, let rest for a couple of minutes, and serve hot.