Have the red snapper thoroughly cleaned and scaled but leave the head and tail intact. Wrap the fish in cheesecloth to facilitate removing it from the pan when cooked.
Place the fish in a large oval baking pan or fish cooker. Add enough water to cover and the remaining ingredients.
Bring to a boil and simmer for about forty-five minutes, until the fish flakes easily when tested with a fork. Very carefully remove the fish from the cooking liquid, using two flat spatulas or pancake turners. Place the first on a long oval platter and remove the cheesecloth carefully.
Chill the fish and serve as a first-course or luncheon dish with Green Mayonnaise.