In a large saucepan, saute onion in butter until tender. Add the broth, carrots and potatoes; bring to a boil. Reduce heat; cover and simmer for 15-20 minutes or until vegetables are tender. Remove from the heat; cool slightly.
Transfer to a blender; cover and process until blended. Return to pan. Stir in the milk, salt and pepper; heat through (do not boil). Garnish with cheese and parsley if desired.