In 4-quart saucepan or Dutch oven, combine water, broth, onion, barley, garlic, salt and pepper. Bring to a boil. Reduce heat to low; cover. Simmer 30 minutes, stirring occasionally. Add broccoli; continue simmering 15 to 20 minutes or until barley and broccoli are tender.
Combine 1/2 cup milk and flour, mixing until well blended. Gradually stir into soup with remaining milk and cheese. Continue cooking over medium heat about 5 minutes or until thickened, stirring occasionally. Add additional water or chicken broth if soup becomes too thick upon standing.
* NOTE: To user Quick QUAKER Barley, substitute 2/3 cup quick barley for medium barley and decrease water to 3 cups. In 4-quart saucepan or Dutch oven, combine all ingredients except milk, flour and cheese. Bring to a boil. Reduce heat to low; cover. Simmer 15 to 20 minutes or until barley and broccoli are tender. Proceed as 2nd paragraph directs.