Combine apple cider, apple brandy, 1/4 cup plus 1 tablespoon brown sugar, honey, cinnamon, ginger, nutmeg, cloves, pepper, and salt in a pot over medium-high heat. Simmer until flavors combine, about 10 minutes.
Pour apple cider mixture into heat-proof mugs. Twist orange zest strips between your fingers to release the essential oils; drop 1 into each mug. Add 1 cinnamon stick to each mug.