Bring a large pot of salted water to a boil. Add the lobsters and cook for about 8-10 minutes until they turn bright red.

Remove the lobsters and allow them to cool slightly. Split them in half lengthwise, remove the meat from the claws, tail, and knuckles, and set aside. Discard the green tomalley and the intestinal tract.

Reserve the lobster shells for stuffing later.

In a large skillet, melt the butter over medium heat. Add the chopped shallot and sauté until softened, about 2-3 minutes.

Add the white wine and cook until it reduces by half, about 3-4 minutes.

Stir in the heavy cream and bring to a simmer. Cook until the mixture thickens slightly, about 5 minutes.

Add the Dijon mustard, lemon juice, and brandy (if using), and stir to combine.

Add the reserved lobster meat, and cook until the lobster is heated through, about 2-3 minutes. Season with salt and pepper to taste.

Preheat your oven to 375°F (190°C).

Stuff the lobster shells with the lobster mixture, ensuring the filling is evenly distributed.

Sprinkle the grated Parmesan and Gruyère cheeses over the top of each stuffed lobster shell.

Place the stuffed lobsters on a baking sheet and bake in the preheated oven for about 10-12 minutes, or until the cheese is melted and bubbly.

Once baked, remove the lobster from the oven and sprinkle with a little paprika for color and chopped parsley for garnish.

Serve immediately with a side of your choice, such as roasted vegetables or a fresh salad.

Enjoy your Lobster Thermidor, a luxurious and indulgent dish perfect for special occasions!