Prep. Spray a 6-quart slow cooker with cooking spray. Place the carrots and potatoes on the bottom of the slow cooker; season with salt and pepper, and set aside.
Prepare the rump roast. Make 12 incisions around the meat and insert a slice of garlic into each. Season the roast with salt and pepper.
Brown the meat. Heat 1 tablespoon olive oil in a large skillet over high heat. Add the roast to the skillet and sear on all sides until browned, about 5 minutes per side. Remove from the skillet and place the roast over the carrots and potatoes. Set aside.
Make the balsamic mixture. In a medium-sized mixing bowl, combine balsamic vinegar, olive oil, beef broth, dijon mustard, brown sugar, oregano, thyme, basil, and nutmeg; whisk until well combined. Slowly pour the balsamic mixture over and around the roast. If needed, use your hands to coat it evenly.
Cook. Cover and cook on LOW for 6 to 8 hours OR on HIGH for 4 to 6 hours.
Let it rest. Remove the pot roast from the slow cooker and let it rest at least 15 minutes before cutting.
Serve. Cut into thin slices and serve with the potatoes and vegetables.