Place the chicken wings, water and salt in a soup kettle.
Bring to rolling boil, and remove any froth which may gather on top.
Reduce heat to simmer and cook covered for 1 1/2 hours.
Strain soup and allow the chicken wings to cool, remove the meat from the bones.
Discard the bones and the skin.
Return the meat to the broth and again place over the heat.
Bring to a simmer again and add the corn and black pepper, add 1/2 c milk and cornstarch to thicken to your liking
Cook for 15 minutes longer.
Stir in the chopped parsley just before serving.
Do not cover after the addition of the parsley or you will spoil its bright green color.
Serve piping hot with oyster crackers.