If using live lobsters, bring a large pot of salted water to a rolling boil. Carefully add the lobsters and cook for 8-10 minutes until they turn bright red. Remove and cool before chopping the meat into bite-sized pieces.

In a large pot, bring water to a boil, add salt, then cook the linguine or fettuccine until al dente, about 8-10 minutes. Reserve a cup of pasta water, then drain and keep warm.

In a large skillet over medium heat, melt 1 tablespoon of olive oil and 1 tablespoon of unsalted butter. Sauté the shallot and garlic for 2-3 minutes until fragrant.

Pour in ½ cup of white wine and scrape the pan to deglaze. Reduce the wine by half, about 3-4 minutes.

Lower the heat and stir in 1 cup of heavy cream and ½ cup of grated Parmesan cheese. Add thyme and the lobster meat, seasoning with salt and pepper. Let sauce thicken for 4-5 minutes.

Add the drained pasta to the skillet and toss until well coated. Adjust thickness with reserved pasta water if needed and add lemon juice and zest.

Serve the creamy lobster pasta hot, garnished with parsley and an extra sprinkle of Parmesan cheese.