Bring a large pot of salted water to a boil. Carefully add the lobsters and cook for 8-10 minutes, or until they turn bright red. Remove from the pot and let them cool slightly before cracking them open.

In a skillet over medium heat, melt the butter. Add the chopped shallots and sauté until they become translucent, about 2 minutes.

Stir in the sliced mushrooms and continue cooking until tender, which should take around 3-4 minutes.

Pour in the white wine and simmer until it’s reduced by half, approximately 3-4 minutes.

Add the heavy cream to the skillet and cook until the mixture thickens slightly, around 3 minutes.

Chop the lobster meat into bite-sized pieces and gently fold it into the sauce along with the paprika and half of the grated Parmesan cheese. Season with salt and pepper to taste.

Preheat the broiler. Fill the cleaned lobster shells with the lobster mixture, sprinkle with the remaining Parmesan, and broil for 3-5 minutes, or until the topping is golden brown and bubbly.