Trim any excess fat from the beef and cut into ¾-inch chunks. Pat dry with paper towels. Season all over with salt and pepper.
In a 12-inch skillet, heat 3 tbsp oil on medium-high. In batches, add the beef to skillet and cook 2–3 min. per side, until browned on 2 sides. Transfer to slow cooker.
Meanwhile, chop the onion and carrots. Halve any large mushroom slices.
To same skillet, add remaining 1 tbsp oil. Add onion and carrots and cook 4 min., stirring often. Add ½ cup water to skillet, stirring and scraping up any browned bits. Transfer to slow cooker, along with mushrooms, garlic, rosemary, tomato paste, broth, and barley. Add ½ cup water. Cover and cook on low 4 hours.
Uncover and stir stew. Cover and cook on low another 2 hours, until barley and beef are tender. Stir in additional ½–¾ cup water to get desired consistency. Season with salt and pepper to taste.