Heat the oven to 400 degrees. Place the sweet potatoes on a baking sheet and prick each one several times with a fork. Bake for 45 minutes until soft when squeezed.
While the sweet potatoes bake, heat a large skillet over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and minced garlic to the skillet. Cook for 3 minutes until the onion softens.
Stir in the tomato sauce, tomato paste, Worcestershire sauce, mustard, salt, and pepper. Simmer for 8 minutes until the mixture thickens slightly.
In a mixing bowl, combine the shredded cabbage, shredded carrot, mayonnaise, and apple cider vinegar. Stir until the vegetables are evenly coated. Season with a pinch of salt and pepper if needed.
Slice each baked sweet potato open lengthwise and fluff the flesh with a fork. Spoon the sloppy joe beef mixture into each potato. Top with a generous scoop of slaw before serving.