Combine cider, cinnamon stick, clove, orange slice, and lemon slice in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Strain cider mixture through a sieve into a bowl; discard solids. Stir in brandy. Serve warm. Garnish each serving with 1 cinnamon stick, if desired.
Steep the cider a day ahead of time, keep it refrigerated, and then reheat just before serving. For a nonalcoholic version, simply omit the brandy.