Melt butter, add veggies, and cook slowly for 5 minutes. Sprinkle flour over veggies & stir well. Add heated broth, and continue cooking over low heat until boils & thickens slightly. Add grated cheese and stir until cheese melts. Gradually add cold milk and heat until scalding hot, but do not boil. Cook at least 10 minutes. Season and sprinkle with parsley when serving. For a more elegant soup-- strain veggies before serving.
Makes 6-8 servings.