1. Bring water to a boil in a fish poacher. Add olive oil, carrots, onions, and celery. Boil for 10 minutes. Lightly salt fish. Place in the boiling water, making sure that it covers the fish (add more water, if necessary). Add potatoes.
2. Cover pot, lower heat, and simmer for 15 minutes or until fish is cooked and opaque. Remove from water carefully and let cool. Cut head and tail off and set aside. When cool, remove skin and lift out the center bone and all other bones. Squeeze fresh lime juice over fish. .
3. Reassemble fish on a fish-shaped platter, adding the head and tail for decoration. Cover with Homemade Mayonnaise. Decorate with the cooked sliced carrots and potatoes. Garnish with parsley. Chill several hours and serve cold.
