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Using a sharp knife, peel the grapefruits, removing all of the bitter white pith. Working over a bowl, cut in between the membranes, releasing the sections into the bowl. Squeeze the juice from the membranes into the bowl.
In a skillet, combine the water, sugar, ginger, star anise, clove and vanilla bean and bring to a boil, stirring, until the sugar is dissolved. Simmer over moderate heat until the syrup is slightly reduced, about 10 minutes. Remove the ginger, star anise, clove and vanilla.
Add the grapefruit and juice to the skillet and cook over moderate heat for 1 minute. Using a slotted spoon, transfer the grapefruit to a serving bowl. Simmer the syrup over moderate heat until reduced to 2 cups, about 5 minutes. Pour the syrup over the grapefruit and garnish with the crystallized ginger. Serve warm or at room temperature, with yogurt.