Bring a large pot of salted water to a rolling boil. Carefully add live lobsters and cook for 8 to 10 minutes, until the shells turn a vibrant red. Once cooked, remove the lobsters and let them cool slightly. Retain the lobster meat for the sauce, ensuring it is cut into bite-sized pieces before setting aside.

In a large skillet, melt 2 tablespoons of unsalted butter over medium heat. Add the chopped shallots and sauté for about 2 minutes until they become translucent. Next, add the sliced cremini mushrooms and continue to cook for an additional 4 minutes, stirring occasionally, until they are tender and have released their moisture.

Pour in ½ cup of dry white wine into the skillet and increase the heat slightly. Allow the mixture to simmer for 3 to 4 minutes, reducing the wine by half. Then, stir in 1 cup of heavy cream, cooking for another 3 minutes, until the sauce has thickened slightly.

Gently fold the reserved lobster meat into the creamy sauce. Add ½ teaspoon of paprika and half of the grated Parmesan cheese, seasoning the mixture with salt and pepper to taste. Stir well.

Preheat your broiler to high. Carefully fill the lobster shells with the lobster and cream mixture, ensuring they are heaped generously. Sprinkle the remaining Parmesan cheese on top. Broil for 3 to 5 minutes, watching closely until the cheese is golden brown and bubbling.