Remove the lobster meat from the tail shell. Slice into bite-size pieces. Set aside.

Bring a large pot of water to a boil.

In a large skillet over medium high heat, add 2 tablespoons of the olive oil, garlic, and chopped lobster to sauté for 5-6 minutes, until the lobster is cooked. Remove the lobster and garlic to a separate bowl.

Add a generous pinch of salt to the boiling water and the pasta to cook until al dente.

Add the remaining tablespoon of olive oil, chopped shallot, and cherry tomatoes. Sauté for 4-5 minutes, until the cherry tomatoes are tender.

Add the Calabrian chili peppers, and tomato paste to cook for 1 minute.

Stir in the heavy cream, whole milk, and ¼ cup pasta water. Stir until a smooth sauce. Season with salt and black pepper to taste.

Add the cooked pasta directly into the sauce, as well as the grated parmesan. Toss until pasta is well coated in the sauce. Add more pasta water, as needed.

Garnish with freshly chopped basil or chives and a drizzle of olive oil to enjoy immediately.