In a large skillet, brown ground beef until no pink remains. Drain, leaving 1 tablespoon of fat in skillet. Scrape browned beef into slow cooker insert.
Add celery and onions to skillet and saute over medium-high heat until translucent, about 3 minutes. Add to beef in slow cooker. Add all other ingredients to slow cooker and stir to combine.
Set slow cooker to Low and cook for 6 - 8 hours, or High for 3-4 hours. Stir occasionally.
You may substitute 1 tablespoon vinegar or pickled banana pepper brine for pepperoncini brine. If using vinegar, regular or apple cider vinegar provide the best flavor.Omit or reduce the added the brown sugar if you like your Sloppy Joes less sweet.Nutrition information does not include rolls for serving.