Step 1: Prepare Lobster - Remove meat from lobster tails, cut into bite-sized pieces and reserve shells for stock.

Step 2: Make Lobster Stock - Heat olive oil, add lobster shells, celery, carrots, onions, peppercorns, bay leaves, and water. Simmer for 1 hour.

Step 3: Cook Lobster - Melt salted butter, sauté lobster pieces until opaque and tender, then remove from heat.

Step 4: Prepare Sauce - Sauté shallot and garlic, add cherry tomatoes until bursting, deglaze with white wine.

Step 5: Combine Sauce Ingredients - Add strained lobster stock to the skillet, simmer and stir in heavy cream.

Step 6: Cook Pasta - Boil salted water, cook linguine until 2-3 minutes shy of al dente, reserve pasta water.

Step 7: Combine - Toss linguine with sauce, add reserved pasta water, and fold in cooked lobster.

Step 8: Serve - Plate the dish, garnish with parsley and black pepper, serve immediately.