Melt the butter and oil in a large skillet over medium heat. Add the onion slices. Stir well.
Make a thyme bundle by wrapping the thyme sprigs with butcher's twine or wrap them in cheesecloth.
Add the thyme bundle to the onions. Cook, over medium heat, stirring occasionally until the onions are deeply caramelized and reduced. Remove the thyme and discard. Season with salt and pepper. Stir.
Keep the onions warm until serving or cover and refrigerate for up to 4 days if making them in advance.
In a large skillet, brown the ground beef and chopped celery.
Stir in the tomato paste and cook for an additional 2-3 minutes, stirring occasionally.
Stir in the brown sugar and apple cider vinegar. Season with salt and pepper.
Cook, stirring occasionally, for an additional 3-4 minutes until the flavors have married and the sloppy joes are heated through.
Serve the sloppy joes on buns and top with slices of Swiss cheese and a helping of thyme-infused caramelized onions.
Tools and equipment;
large skillet, wooden spoon, measuring cups, measuring spoons, butchers twine or cheesecloth, chef's knife, cutting board.
The thyme-infused caramelized onions may be made in advance and refrigerated for up to 4 days (covered). Reheat before serving.