Using a very sharp knife, peel the grapefruit and oranges, discarding the skins (be sure to remove all of the white pith). Slice the fruit into 1/4-inch rounds, removing pits as you go. Set aside in a medium non-reactive bowl.

In a medium non-reactive pan, combine the water, sugar, lemon juice. Scrape the seeds from the vanilla bean and add the seeds and bean to the liquid. Bring to a gentle simmer for 5 minutes. Thinly slice 6 of the basil leaves and toss over the citrus rounds.

Remove liquid from heat and strain over the citrus and basil. Refrigerate until chilled.

Serve the chilled fruit and liquid over Lemon Sorbet or Vanilla Ice Cream. Garnish with fresh basil.