If your slow cooker has a stove top safe insert then heat 1 1/2 tablespoons olive oil over medium heat, otherwise do in a medium skillet and transfer to slow cooker. Season beef with salt and pepper and brown pieces in olive oil until browned on all sides, about 6 minutes.
Add remaining olive oil and garlic and sauté until fragrant. Place insert into slow cooker or transfer to slow cooker add thyme and 2 cups beef broth and scrape sides and bottom of pan to release browned bits. Transfer broth to slow cooker.
Add potatoes, squash, and barley to slow cooker with 2 cups water and remaining 2 cups of beef broth. Cover and cook on high until meat is very tender and liquid is mostly absorbed (about 4 hours on high or 8 hours on low). Using 2 forks shred beef. Season with salt and pepper.