In a large saucepan or Dutch oven, stir together the beef broth, thyme, salt, and black pepper. Add barley and carrots. Bring to boiling; reduce heat. Simmer, covered, for 5 minutes.
Add sugar-snap peas or beans, leek, and red or green sweet pepper. Bring mixture to boiling; reduce heat. Simmer, covered, for 5 minutes more or until vegetables and barley are tender. Add the tomatoes and heat through. Makes 8 side-dish servings.
When slicing the leek, use the white portion and about 1 inch into the green tops of the leek.