Remove zest from 1 grapefruit and set aside; you should have about 1 teaspoon.

Cut thin slices off top and bottom of a grapefruit and set on a cutting board.

Slice down along the curve of the fruit, removing all skin and white pith, and cutting all the way to the flesh.

Working over a bowl, cut along each side of the membranes to release the sections, allowing them to fall into the bowl along with any juice.

Repeat with remaining grapefruit. Discard any seeds and set the bowl aside.

Combine honey, sugar, ginger, star anise, cinnamon sticks and reserved grapefruit zest in a large saucepan.

Add 1 cup water and bring to a boil over high heat, stirring to dissolve sugar.

Reduce heat and simmer for 10 minutes.

Add grapefruit segments and juice and gently simmer just until warm, 2 to 3 minutes.

Using a slotted spoon, transfer segments to a bowl; set aside.

Return poaching liquid to a simmer, adjust heat and simmer, stirring occasionally, until reduced to about 3/4 cup, 20 to 25 minutes.

Remove ginger and spices and spoon syrup over grapefruit.

Cover and refrigerate until chilled, at least 1 hour and up to 3 days.