Bring a large pot of salted water to a boil over high heat. Carefully add the live lobsters and boil them for 8–10 minutes until they turn bright red. Once cooked, remove the lobsters and let them cool on a plate. When cool enough to handle, crack open the shells and extract the tender meat, setting it aside for later use.

In a large skillet, melt 3 tablespoons of butter over medium heat. Add the chopped shallots and sauté for about 2 minutes until they become translucent and fragrant. Next, add the sliced mushrooms and cook for an additional 5–7 minutes until they are tender and starting to brown.

Pour in 1 cup of white wine into the skillet, allowing it to simmer and reduce by half, which takes approximately 5 minutes. Stir in 1 cup of heavy cream, mixing well, and allow the sauce to thicken over medium heat for about 3 minutes.

Chop the lobster meat into bite-sized pieces and gently fold it into the creamy sauce. Add 1 teaspoon of paprika along with half of the grated Parmesan cheese, mixing until everything is well combined. Season the mixture with salt and pepper to taste.

Preheat your broiler to high. Carefully transfer the lobster filling back into the cleaned lobster shells, and top with the remaining Parmesan cheese. Place the shells on a baking sheet and broil for 3–5 minutes until the tops are golden brown and bubbly.

Once broiled to perfection, remove the lobster thermidor from the oven and let it cool slightly. Serve hot, paired with a crisp salad or crusty bread.