Begin by removing the meat from the lobster tails. Chop the lobster into bite-sized pieces and set them aside. Save the shells for making a rich lobster stock.

In a medium pot, heat olive oil over medium heat. Add lobster shells and sear for 5 minutes until bright red. Add celery, carrots, halved onion, water, black peppercorns, and bay leaves. Bring to a boil, then simmer on low for 1 hour.

Strain the stock through a fine-mesh sieve into a bowl, discarding solids. Let it cool slightly.

In a large skillet, melt salted butter over medium heat. Add chopped lobster and sauté for 4-5 minutes until opaque. Remove the lobster and set aside.

In the same skillet, add minced shallot and garlic, sauté for 2 minutes. Add halved cherry tomatoes and cook for about 10 minutes until they burst. Deglaze with white wine.

Pour in strained lobster stock into the skillet. Bring to a gentle simmer and gradually stir in heavy cream. Allow to thicken slightly.

Boil a large pot of salted water. Cook linguine 2-3 minutes shorter than package instructions for al dente. Reserve 1 cup of pasta water before draining.

Add cooked pasta to the skillet with the sauce. Toss gently, adding reserved pasta water until combined. Fold in sautéed lobster, adjusting seasoning as needed.

Garnish with chopped parsley and black pepper. Serve immediately.