Use kitchen shears to cut through the top of the lobster shells. Carefully pull the meat out and cut it into bite-sized chunks. Pat the lobster meat dry with paper towels to ensure it sears properly later. Season lightly with salt and pepper.

Bring a large pot of salted water to a boil. Cook the linguine according to the package instructions until it is al dente. Before draining, reserve at least 1 cup of the starchy pasta water. Drain the pasta and set it aside.

In a large skillet over medium heat, melt 2 tablespoons of butter. Add the lobster chunks and cook for 2-3 minutes until they turn opaque and slightly pink. Remove the lobster from the pan and set it aside on a plate. In the same skillet, add the remaining butter, diced shallots, and minced garlic. Sauté for about 2 minutes until fragrant and translucent.

Pour the white wine into the skillet to deglaze, scraping up any browned bits from the bottom. Let the wine reduce by half. Pour in the heavy cream and bring to a gentle simmer. Whisk in the Parmesan cheese until melted and smooth. Stir in the lemon zest, lemon juice, and red pepper flakes.

Add the cooked pasta and the lobster meat back into the skillet. Toss everything together using tongs to ensure the sauce coats every strand of pasta. If the sauce is too thick, add a splash of the reserved pasta water. Season with more salt and pepper if needed. Garnish heavily with fresh parsley and serve immediately.