Use a vegetable peeler to cut a three-inch strip of orange peel, pressing lightly so you get mostly peel with very little of the bitter white pith underneath.

Pour the apple cider into a medium saucepan and set it over medium heat. Add the cinnamon sticks, whole cloves, star anise, and orange peel strip.

Watch the heat carefully. You want the cider to reach a gentle, steady simmer where small bubbles rise slowly to the surface. Do not let it come to a hard boil. Reduce the heat to medium-low the moment it starts to bubble actively.

Simmer uncovered for twenty minutes, stirring once or twice. After about fifteen minutes the cider will deepen in color slightly and smell strongly of cinnamon and clove. Taste it near the end and stir in brown sugar or honey now if it needs a little sweetness.

Remove the pan from the heat. Set a fine mesh strainer over a heat-safe pitcher or large measuring cup and pour the cider through to catch all the whole spices and orange peel.

For hot cider: ladle immediately into mugs and garnish each with a fresh cinnamon stick. For cold cider: let the strained cider cool to room temperature, then refrigerate until fully chilled and pour over ice to serve.