Stir in 1 cup hot broth mixture; reduce temperature to medium. Cook uncovered, stirring frequently, until broth is absorbed; repeat with 3 more cups broth, adding 1 cup at a time. Stir in remaining 1 cup broth (discard thyme sprigs). Cook, stirring frequently, until almost all liquid is absorbed; discard bay leaves. Remove from heat; fold in roasted squash. Cover and let stand about 5 minutes or until barley is just tender and liquid is absorbed. Fold in arugula. Sprinkle with cheese and pepper. Serve immediately.