Cut a thin slice off the top and bottom of each grapefruit with a small serrated knife. Working from the top of the fruit to the bottom, follow the curve of the fruit to cut away peel and white pith. Working over a bowl to catch the juices, use a paring knife to slice along one side of each segment, separating it from the thin membrane. Slice down the other side to remove the whole segment. Repeat with remaining segments; set aside grapefruit with its juice.

In a large saucepan combine 1 1/2 cups water, honey, sugar, zest, ginger, cinnamon and star anise. Bring to a boil, stirring to dissolve honey and sugar, then reduce heat and simmer, uncovered, for 10 minutes. Add grapefruit segments with their juice and cook at a very gentle simmer for 2 to 3 minutes. Using a slotted spoon, transfer grapefruit segments to a bowl; set aside. Bring poaching liquid back to a boil and boil until mixture is reduced to 1/2 cup. Spoon syrup over grapefruit segments, cover and chill for 1 hour before serving.