In the work bowl of a food processor, place broccoli stems. Pulse until roughly chopped.
Transfer broccoli mixture to a medium sauce pot. Stir in all remaining ingredients. Bring mixture to a simmer over medium-high heat. Cook, stirring occasionally, until broccoli is crisp-tender, about 20 minutes. Remove from heat and let cool.
Divide mixture among clean glass jars and refrigerate overnight before serving. Store refrigerated for up to 2 weeks.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/broccoli-apple-relish/