Place potatoes, onions, celery and salt in water to cover in a large pot. Simmer until tender, about 15 minutes.
Purée just until chunky in blender or food processor fitted with a metal blade. Return to soup pot; add half-and-half, butter and cheese.
Stirring, simmer until piping hot. (Do not boil) Garnish with parsley if desired. Good served with cornbread.
Makes: 8 to 10