Rinse the insides of the lobster shells, then break them up into very small pieces. In a large saucepan, heat the pure olive oil. Add the lobster shells and cook over moderately high heat, stirring often, until the shells start to brown, about 5 minutes. Add the shallots and thyme sprigs and cook, stirring, until the shallots start to brown, about 3 minutes. Reduce the heat to moderate and add the tomato paste. Cook, stirring, until the tomato paste starts to stick to the bottom of the pan, about 3 minutes. Add the Cognac and simmer, scraping up the browned bits from the bottom. Add the water and a pinch of salt and bring to a simmer. Cook the lobster stock over low heat until reduced to 2 cups, about 20 minutes.