Instructions:
Cook the beef: Place the beef chuck roast in a slow cooker and cook on High for 4-5 hours, or until tender. Add barley and bay leaf during the last hour of cooking.
Prepare the vegetables: Remove the cooked beef from the slow cooker and chop it into bite-sized pieces. Discard the bay leaf. Set the beef, broth, and barley aside.
Sauté the vegetables: Heat oil in a large stockpot over medium-high heat. Sauté the carrots, celery, onion, and frozen mixed vegetables until tender, about 5-7 minutes.
Combine ingredients: Add water, stewed tomatoes, beef bouillon cubes, sugar, black pepper, and the beef-barley-broth mixture to the stockpot. Bring to a boil, then reduce heat and simmer for 10-20 minutes.
Season and serve: Season the soup with salt and pepper to taste before serving.