Remove the lobster meat from the shell. Using shearing scissors, turn the tail over and cut down the middle. Peel the shell away and remove the meat. Cut the lobster meat into large pieces. Set the meat and the shell to the side.
Begin by making the lobster stock. On a high heat in a large pot, bring 3 tablespoons of olive oil to heat. Add the lobster shells to the pot and fry until they turn red. Add the celery, carrot, onions and tomato paste to the pot and fry for an additional 1 minute or until the tomato paste turns a deep red colour. Add the water to the pot along with the black peppercorns, bay leaves and generous amount of salt. Bring to the boil then reduce the heat so the stock is at a gentle simmer. Simmer with the lid partially on for 1 hour.
Strain the stock through a fine mesh strainer and set to the side. There will be more stock than is needed for this recipe. Freeze the remaining stock and use in any recipe that calls for seafood stock.
On a low heat in a large pan, add the butter and remaining half tablespoon of butter. When the butter is melted and slightly foaming, add the lobster and poach it on a very low heat for 5 minutes until no longer glassy. The lobster meat should be tender and pink. Scoop out of the pan with a slotted spoon and set to the side.
Turn the heat to medium and fry off the shallots and garlic for 2 minutes, stirring often. Add the cherry tomatoes to the pan and cook for 10 minutes or until they have burst open and created a lovely jammy sauce.
Turn the heat to high and add the white wine and lobster stock to the pan. Reduce the sauce for 8 minutes. Add the cream to the sauce and stir through for 1 - 2 minutes or until well combined.
While the sauce reduces, cook the pasta. Bring a large pot of heavily salted water to the boil. Cook the pasta for 2 – 3 minutes less than the instructions on the packet as it will continue to cook when we stir it through the sauce. Drain and reserve up to 1 cup of pasta water.
On a low heat, stir the pasta through the sauce while slowly incorporating the pasta water. Do this step gradually as you may not need all of the pasta water. Gently fold through the lobster meat. Finish off by sprinkling over the fresh parsley and a crack of black pepper. Serve immediately.