In a large saucepan, combine the first seven ingredients; bring to a boil. Reduce heat; simmer, covered, 10-15 minutes or until potatoes are tender. Stir in broccoli; return to a boil.
In a small bowl, whisk flour and milk until smooth; stir into soup. Cook and stir 2 minutes or until thickened. Remove from heat; cool slightly.
Process in batches in a blender until smooth. Return to pan; heat through. Sprinkle servings with cheese and parsley.