In a small bowl whisk together the mayonnaise, the yogurt, the Cognac, the ketchup, the lemon juice, and salt and pepper to taste and chill the sauce, covered. Plunge the lobsters into a large kettle of boiling salted water and boil them, covered, for 10 minutes. Transfer the lobsters with tongs to a bowl and let them cool until they can be handled. Crack the shells, remove the meat, and cut it into 3/4-inch pieces. Transfer the lobster meat to a large bowl and chill it, covered. The lobster cocktail may be prepared up to this point 1 day in advance.
Halve the mangoes by cutting just to the sides of each pit and, using a 3/4-inch melonball cutter, scoop the flesh from the mango halves. (There should be about 2 cups.) To the lobster meat add the mango balls, the celery, the whole endives, trimmed and sliced thin crosswise, the minced
chives, and the sauce and toss the mixture until it is combined. Divide the lobster mixture among 12 chilled small glasses an garnish each serving with 1 of the endive leaves and 2 of the whole chives.
Recipe courtesy of Gourmet Magazine