Make the cups: Cut the tops off of each apple and hollow out the insides, leaving 1/4-inch border around the edge. Brush each apple with lemon juice to prevent browning.
Make the boozy cider: Pour apple cider into a large stockpot on medium-low heat. Add cloves, cinnamon, anise, nutmeg, lemon peel and maple syrup. Stir to combine, and bring heat up to medium-high until the cider boils. Turn down to a simmer and add bourbon. Pour 3/4 cup of cider into each apple and finish with a cinnamon stick. Serve while warm.