Combine vinegar, sugar, salt, cardamom, orange peel, celery, onion, apples, and 2 cups water in a low-sided, 6-quart saucepan. Set over medium-high heat; bring to a boil.
Reduce heat to a simmer, and cook until apples are tender and most of the liquid has been absorbed, 30 to 40 minutes.
Stir in cranberries; cook until they begin to pop, 10 to 15 minutes. Remove pan from heat.
Transfer to a large bowl, set over an ice bath to chill.
Store in an airtight container, refrigerated, up to 4 weeks.