For Cranberry Topper, in food processor cover and pulse cranberries 5 times to coarsely chop (or coarsely chop by hand). Transfer to bowl.
Cut peel from oranges. Section oranges over bowl to catch juice. Add sections and juice to cranberries. Stir in celery, onion, sugar, lemon juice, and ginger. Cover and refrigerate at least 1 hour or up to 2 days.
Toss arugula with mint and oil. Top with cranberry mixture. Serves 8.