In the food processor bowl, pulse four orange wedges until peel is no longer in large pieces. Add half the cranberries and pulse until finely chopped but not puréed. Transfer to medium bowl.
Repeat Step 1 with remaining oranges, then add remaining cranberries. Transfer second chopped mixture to same medium bowl.
Stir in ½ cup white sugar and one pinch ground cinnamon.
Cover and chill for at least an hour (see Note). After one hour, taste and add more sugar, if necessary.