Clean and wash fruit. Cut off the top quarter and slice a thin bevel off the bottom of the fruit, so they stand up straight.
Using a grapefruit knife, carefully remove and save the flesh and juice; be careful not to cut through the bottom. Stand the rinds on a plate or cookie sheet and freeze until solid.
Combine scooped out flesh and juice with essential oil in a food processor or blender; pulse until mostly pureed then press mixture through a fine-mesh strainer.
Stir in water; add sugar or honey one tablespoon at a time to taste. Pour mixture into large roasting pan or baking dish, large enough that the liquid isn’t more than one inch deep.
Freeze for one to three hours. Remove mixture from freezer every half hour and scrape with two forks to break up ice.
When the granita is frozen, rake until glittery. Scoop into frozen lemon or orange shells and serve.
Tip: For a lemon-mint granita, try four drops of Spearmint oil with lemon juice and fruit, and garnish with a sprig of fresh mint.