Place the beef, barley, carrots, celery, onion, and garlic in the slow cooker.
In a small bowl, whisk the tomato paste into 1 cup of the beef broth until smooth, then pour it into the slow cooker.
Add the remaining beef broth, thyme, bay leaves, salt, and pepper. Stir to combine.
Cover and cook on low for 7 to 8 hours, until the beef is tender and the barley is cooked through.
Remove the bay leaves before serving.