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Cut the half apple into thin slices.
Pour the apple juice into a saucepan and add the apple slices, the cinnamon stick, and the star anise.
Heat over low heat for 8 to 10 minutes, without bringing it to a boil.
Remove from the heat and let steep for 2 minutes.
Add the apple-cinnamon balsamic vinegar and stir.
Taste it and add a little honey if you'd like a sweeter drink.
Serve hot with a few apple slices and the cinnamon stick.
