Thoroughly rinse and dry apples. Core the apples, and slice them into 1/8-1/4 inch wedges. Add the apple wedges to an airtight glass jar. Rest a fine mesh sieve on the lip of the jar. Set aside.
Add all other ingredients to a medium-sized saucepan and bring to a boil. Remove the saucepan from the heat and pour the liquid through the sieve and onto the apples. Fill the jar to the top so that all apple slices are covered with brine. Tuck the cinnamon sticks into the jar along with the apples. Allow the brine to cool to room temperature, then seal the jar and transfer to the refrigerator. When stored in an air tight container and kept refrigerated, the pickled apples will keep for about two weeks.