Prepare Lobster: Remove the meat from lobster tails, slicing through the shell to extract chunks. Chop into bite-sized pieces and set aside; save the shells for stock.

Make Lobster Stock: Heat olive oil in a large pot over medium heat; sear lobster shells until bright red (about 5 mins). Add celery, carrots, onions, water, black peppercorns, and bay leaves. Bring to a boil, then simmer for 1 hour.

Strain the Stock: Strain the stock through a fine-mesh sieve into a bowl, discarding solids. Allow to cool slightly.

Cook Lobster: Melt salted butter in a large pan over medium heat. Sauté lobster pieces for 4-5 minutes until opaque. Set aside.

Prepare Sauce: In the same pan, sauté shallot and garlic for 2 minutes. Add cherry tomatoes, cooking until they burst (about 10 mins). Deglaze with white wine, reducing by half.

Combine Sauce Ingredients: Stir in strained lobster stock and simmer on low. Add heavy cream, stirring until creamy and combined.

Cook Pasta: Boil salted water in a separate pot, add linguine and cook 2-3 minutes shy of al dente. Reserve 1 cup of pasta water before draining.

Combine: Toss drained linguine into the sauce, adding reserved pasta water gradually until sauce clings. Fold in lobster, tasting for seasoning.

Serve: Garnish with parsley and black pepper. Serve immediately.