Peel, quarter, and core pears and apples. In a food processor, finely grate fruit (in batches if necessary), then transfer to a 5- to 6-quart slow cooker. Stir in dark-brown sugar, salt, and cinnamon stick. Cover and cook on high, 4 hours.
Remove cinnamon stick and reserve. Transfer mixture to processor (in batches if necessary) and process until smooth. Return to slow cooker, along with cinnamon stick, and cook on high, uncovered, until mixture is thick and browned, 4 hours. Discard cinnamon stick and let mixture cool. Transfer to airtight containers and refrigerate, up to 3 weeks, or freeze, up to 3 months.