Take your orange slice and stud it by pushing the whole cloves directly into it.
In a small saucepan, combine the apple cider, the clove-studded orange slice, the cinnamon stick, allspice berries, and ginger slice. Place the saucepan over medium-low heat and stir in the brown sugar.
Bring the mixture to a gentle simmer, but do not let it boil as boiling can make the spices bitter. Reduce the heat to low, cover, and let it gently infuse for at least 15 minutes.
Stir in the brandy, rum, or applejack. Strain through a fine-mesh sieve into a heatproof mug or glass, retaining the cinnamon stick.
Grate a tiny pinch of fresh nutmeg over the top and garnish with the reserved cinnamon stick.