Pour the apple cider into a large pot or slow cooker.
Cut 1 medium orange into 1/4-inch-thick rounds. Cut 1 1/2 inches ginger crosswise into 1/4-inch-thick slices. Add both to the slow cooker.
Add cinnamon sticks, cloves, star anise, orange slices, nutmeg, and ginger if using.
Simmer gently over low heat for 20–30 minutes. Do not let it boil.
Strain out the spices and orange slices.
Serve hot in mugs. Garnish with a cinnamon stick or orange slice if desired.
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For an adult version, stir in rum, brandy, or bourbon before serving.