In a large pot, bring the water to a boil. Add the onion, carrot, thyme, and bay leaf. Reduce the heat to a minimum and poach the lobster in this broth for 10 minutes. Remove the lobster and let it cool. Shell the tail and claws. Keep the coral and shell that will be used to prepare the base of the velouté. In a large pot, sauté the onion and tomatoes. Once colored, add the lobster’s coral and shell, coarsely chopped, and sauté everything for 3 minutes over low heat. Pour in the cognac and white wine and let reduce over low heat for 10 minutes. After a slight evaporation of the alcohol, incorporate the 15% cream and milk. Continue cooking over low heat and let reduce for 30 minutes. Pour into the blender. Mix everything and filter the preparation to remove the shell residue.