Cut langouste or lobster tail in pieces and split body in half lengthwise. Remove coral and reserve; remove the sandy pocket.
Season tail pieces and body with salt and freshly ground black pepper. Heat oil in a large thick-bottomed frying pan; add tail pieces and body, and sauté, stirring from time to time, until coloured; drain; add butter and mirepoix bordelaise.
Moisten with dry white wine and enough white stock (chicken or veal) to cover pieces. Add tomatoes, garlic, cayenne and bouquet garni. Simmer gently for about 20 minutes. Remove and drain tail pieces only, and place them on a heated serving dish.
Reduce cooking liquid over a high heat, and blend coral together with beurre manié (