Cut the apples in half crosswise and scoop most of the pulp, leaving a thick wall. Make sure apple halves stand straight. If not, slice off a little bit of the rounded ends.
Add the cloves, cinnamon sticks, and star anise to a large saucepan over medium heat. Lightly toast the spices in the pan for 1 minute.
Add the orange juice and apple cider, and simmer for 10 minutes. Do not boil.
Reduce the heat to low and add the spiced rum and the rum extract.
Ladle the cider into the apple halves and garnish with cinnamon or a strip of orange peel, if desired. To keep warm, the cider can stay on very low heat until serving.