Combine apple cider, allspice, 2 cinnamon sticks, and star anise pod in a small saucepan; bring to a simmer over medium. Simmer until reduced to 1/2 cup, 7 to 10 minutes. Remove from heat. Transfer to a glass bowl or jar with a lid, and cool completely. Cover and chill 24 hours.
Pour cider mixture through a fine wire-mesh strainer into an ice-filled cocktail shaker; discard solids. Gently pour 4 oz. spicy ginger beer into each of 2 chilled, ice-filled copper mugs. Add gin and vinegar to cider mixture in cocktail shaker; shake vigorously until thoroughly chilled, about 15 seconds. Strain evenly into copper mugs; garnish each with thin slices of Honeycrisp apple and a cinnamon stick.