Carefully remove the meat from the lobster tails, chop into bite-sized chunks, and reserve shells for stock.

In a large pot, heat olive oil over medium heat, add lobster shells and sauté until red. Stir in vegetables and tomato paste, add water, peppercorns, and bay leaves; simmer for one hour.

In a skillet, melt butter and cook chopped lobster for 4-5 minutes until opaque.

In the same skillet, sauté shallot and garlic, then add cherry tomatoes. Cook until bursting, add wine and reduce, then stir in lobster stock and cream.

Cook linguine in salted water until al dente, reserving pasta water before draining.

Combine drained pasta with the sauce, adding reserved pasta water as needed, then fold in lobster meat.

Plate the pasta, garnishing with parsley and black pepper; serve immediately.