Whisk ¼ cup wine, 3 tablespoons oil, 1 ½ tablespoons kosher salt, Italian seasoning, vinegar, ½ teaspoon black pepper, and garlic salt together in a bowl; pour into a resealable plastic bag.
Add rump roast, coat with marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 8 hours or overnight.
Remove roast from marinade and shake off excess. Discard remaining marinade.
Melt butter in a large skillet over medium-high heat. Add roast; sear, turning to brown all sides, about 10 minutes.
Place roast in a slow cooker. Add carrots, celery, broth, onion, parsley, remaining ½ cup wine, remaining 4 tablespoons oil, garlic, salt, and pepper.
Cover and cook on Low heat until roast is fall-apart tender, 9 to 10 hours. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).
