Put oranges in a food processor fitted with a metal blade, or a blender, and pulse several times until coarsely chopped, or coarsely chop with a knife by hand.
Place chopped orange, cider, cranberry juice cocktail, 2 cinnamon sticks and brown sugar in a large heavy saucepan over medium-high heat.
Cook, stirring often until hot, about 8-10 minutes.
Using a large sieve, strain mixture and return to saucepan.
Note: If not using immediately, cool, cover and refrigerate for up to 1 day.
Reheat before serving.
Cider and also be frozen, defrosted and reheated.
To serve, pour into mugs or cups and garnish each serving with a cinnamon stick and 1 orange slice.