In a stovetop-safe 5 to 6-quart slow cooker, place bowl over medium-high heat on stove. Add meat and cook for 5 minutes, stirring occasionally, or until browned on all sides; remove with slotted spoon and set aside.
Place carrots and onion in slow cooker bowl and cook for 5 minutes, stirring occasionally, or until browned. Add mushrooms and cook for another 7 minutes. Stir in tomato paste and cook for 2 minutes, stirring constantly. Remove bowl from stove and place in slow cooker.
Add beef, broth, tomatoes, and 1/2 teaspoon thyme to slow cooker. Cook on HIGH for 4 hours or on LOW for 7-1/2 hours. Stir in barley for last 50 minutes of cooking time. Stir in remaining 1/4 teaspoon thyme, salt and pepper immediately before serving.