Wash the apples, slice them into quarters and discard the stems. Place the quartered apples at the bottom of a large pot and add the water, sugar, ground cinnamon, nutmeg, cloves, and cinnamon stick and stir to combine. Bring the mixture to a boil over medium heat. Allow the mixture to boil lightly, uncovered, for 1 hour, stirring occasionally. Lower the heat to a simmer and allow the mixture to simmer, uncovered, for another hour.
Cut two 18-inch by 18-inch pieces of cheesecloth and layer them on top of each other. Place a large metal colander over a large bowl, and line the colander with the cheesecloth. Remove the cider mixture from the heat and *carefully* pour the cider mixture into the lined strainer, then allow to cool and drain for 1 hour.
Pick out the cinnamon stick and discard it. Fold up the edges of the cheesecloth to create a pouch, hold the pouch over the strainer, and continue to twist gently until the cider stops dripping out of the pouch. You can also squeeze the pouch with tongs or your spare hand while twisting to get more juice out of the apples, but take care not to tear the cheesecloth. Once the juices are only dripping out instead of coming out in a stream, you can set the apple pulp aside to either compost it or eat it (just be wary of the whole cloves).
You can reheat the cider to serve it warm, or pour the cider into an airtight container, like a very large mason jar, cool to room temperature, cover, and refrigerate to serve chilled. Will keep in an airtight container in the refrigerator for up to 2 weeks.