Pat the pork roast dry with paper towels. Mix the salt, pepper, paprika, thyme and sage together and rub it into the pork roast on all sides.
Heat a large skillet on medium and add the olive oil, coating the bottom. Place the pork roast into the skillet and sear for 2-3 minutes on all sides, getting a deep golden crust.
Add the onion, apples, and carrots to the slow cooker base. Sprinkle the garlic over the top.
Place the seared pork roast on top of the onions, apples, and carrots.
Whisk together the chicken broth, apple cider vinegar, and brown sugar. Pour the mixture over the roast and veggies. Brush the Dijon mustard over the roast.
Secure the lid and cook for 4-5 hours on high or 6-7 hours on low until the roast can be easily pierced with a fork and the internal temperature reaches 145°F. Baste the roast with the liquid a couple times through cooking.
Place the vegetables, apples, and roast onto a serving dish and allow the roast to rest for 10 minutes before cutting.
If the gravy is too thin, mix a 2 tablespoon cornstarch slurry and leave uncovered in the slow cooker to thicken.
Serve the pork roast with the gravy on top and alongside the carrots and onions.