Combine first 8 ingredients in a small Dutch oven; bring to a boil. Reduce heat; cover and simmer 20 minutes. Remove from heat, and cool slightly.
Puree mixture in a food mill or blender, discarding any vegetable hulls. Return vegetable puree to Dutch oven. Gradually add milk, beating well with a wire whisk. Stir in salt. Place over medium heat, and cook until thoroughly heated. (Do not boil.) Ladle into warm soup bowls, and serve immediately. Garnish each serving with parsley, if desired.