Make the slaw: In a medium bowl, combine the coleslaw mix, apple cider vinegar, olive oil, mustard, salt, and pepper. Toss well, then cover and refrigerate until ready to use.
Make the sloppy joes: Heat the oil in a large, high-walled pan over medium heat. When the oil is shimmering, add the onion and sauté for 2–3 minutes, or until translucent. Add the garlic, chili powder, paprika, thyme, tomato paste, and dates. Stir to combine and cook for 2–3 minutes, until the tomato paste begins to brown.
Add the turkey and sauté until cooked through, about 3–5 minutes, stirring throughout. Add the tomato sauce, apple cider vinegar, and Worcestershire sauce. Stir to combine.
Add the shredded carrots and zucchini and cook down into the sauce, about 3–5 minutes. Season with salt, pepper, and hot sauce, if using.
Scoop the sloppy joe mixture onto toasted buns and top with the slaw.