Wash clams. Make sure they are all unopened. Place in a large stock pot. Add enough water to cover the bottom of the pot. Steam clams over medium heat until clams open. Discard any unopened clams. Place a coffee filter in a strainer over a bowl. Pour clams and liquid into strainer. Allow to sit and cool.
Rinse stock pot of any sand. Rinse and finely chop the salt pork (you may substitute bacon). Fry the salt pork until slightly brown and crisp. Add onions and celery. Cook until slightly tender. Add flour and stir to make a roux. Add potatoes, reserved clam liquid and enough water to cover. Add seasonings. Cover and simmer until potatoes are tender. Add reserved clams and half and half. Cook until heated through. Do not boil!
Serve in individual soup bowls or a soup tureen garnished with chopped parsley.