01 - Cook pasta in a large pot of generously salted boiling water until al dente. Drain well, reserving 1/2 cup of the pasta cooking water for later use.
02 - In a large skillet, melt butter over medium heat. Add finely chopped shallots and sauté for 2-3 minutes until translucent. Stir in minced garlic and cook for an additional minute until fragrant.
03 - Carefully pour Cognac into the skillet. Allow it to simmer for 1-2 minutes to reduce slightly. Exercise caution as the alcohol may ignite.
04 - Incorporate heavy cream, fish or lobster stock, Dijon mustard, lemon juice, and cayenne pepper into the skillet. Stir thoroughly and simmer for 4-5 minutes until the sauce begins to thicken.
05 - Add grated Gruyère and Parmesan cheeses to the sauce. Stir continuously until the cheeses are fully melted and the sauce is smooth. Season with salt and freshly ground black pepper to taste.
06 - Gently fold the chopped lobster meat into the sauce. Cook for 2-3 minutes, just long enough to warm the lobster through.
07 - Add the cooked pasta to the skillet with the sauce. Toss gently to ensure the pasta is evenly coated. If the sauce seems too thick, gradually add the reserved pasta water, a tablespoon at a time, until a silky consistency is achieved.
08 - Remove the skillet from the heat. Stir in the chopped fresh parsley and lemon zest.
09 - Serve the Lobster Thermidor Pasta immediately. Garnish with additional cheese and parsley if desired.