Combine the water, honey, zests, ginger, cinnamon, and allspice berries in a heavy saucepan and bring to a boil. Cover, reduce heat, and simmer, until cinnamon is unfurled and mixture is aromatic, about 10 minutes. Strain.
Meanwhile, cut peel and white pith off the grapefruits and oranges with a serrated knife. With a sharp paring knife, cut between the membranes, catching any juices in a bowl, to release segments. Add the juices to the honey-spice mixture. Put the fruit segments in a bowl.
Pour the hot liquid over the citrus, add the grenadine or vermouth and stir to combine. Serve the citrus compote with biscotti.
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