Add the apples, tangerines, cinnamon sticks, and cloves to a Dutch oven or stockpot.
10 large apples, 3 tangerines, 4 cinnamon sticks, 2 teaspoons whole cloves
Cover with water by 2 inches and bring to a boil. Reduce to a simmer, cover, and cook for 2 hours. Check occasionally to ensure it is still simmering.
2-3 quarts water
Use a potato masher to mash the fruit and release the juices.
Cover and simmer for 1 more hour.
Line a large colander with cheesecloth and place it over a large bowl.
Ladle or pour the cider mixture through the strainer. Press down on the solids with a spoon to extract as much juice as possible.
Wipe out the pot and return the cider to the pot. Stir in the brown sugar until dissolved.
½ cup brown sugar
Keep warm on the stove until serving.