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. Chop into large pieces.
To create the lobster stock, add the lobster tail shells into a large pot with 3 whole garlic cloves, 2 thyme sprigs and 5 cups of water. On a high heat, bring to the boil then reduce the heat to low – medium or until the stock is at a slow simmer. Pop the lid on and simmer for 1 – 2 hours. Through a fine mesh strainer, strain the stock and set to the side. Discard of the shells and aromatics. You should be left with 4 cups of stock. If you have any extra, store in the freezer and use in any recipe that calls for seafood stock.
In a heavy based saucepan on a low heat, melt the butter. Drizzle with olive oil and then add the lobster meat. Cook on a very low heat so there is only a slight bubble to the butter as we want to slowly poach the lobster meat. Cook for 3 – 5 minutes or until the lobster meat turns pink. Using a slotted spoon, remove the lobster meat from the pan, ensuring you leave as much of the butter in the pan as possible.
Turn the heat to medium – high and add the celery, carrots, onion, bay leaf and remaining garlic cloves and thyme sprigs to the pot. Cook for 5 minutes while stirring occasionally. Turn the heat to high and add the tomato paste. Cook for 3 minutes or until the tomato paste turns a deep red brick colour and is almost sticking to the bottom of the pan. Deglaze the pan with white wine and cook until 80% of the liquid has been absorbed. Add 4 cups of the lobster stock to the pot and bring to a simmer. Cook for 30 minutes.
Using a hand held blender, blend the soup until you have a smooth consistency. You can also do this step in a blender but just be careful and ensure your soup has slightly cooled before blending.
Stir through the cream. Sprinkle over the lobster meat and chives and finish with a crack of black pepper.