If using fresh clams, rinse them under running water to clean the shells and set aside. If using frozen clams, thaw them in the refrigerator overnight and chop them roughly, if necessary. Canned clams can be used right out of the can.
Put the cubed salt pork (or bacon) into a heavy-bottomed stock pot or Dutch oven over medium heat. Cook until it has begun to get brown and crispy. Add the butter, minced onion and celery and cook for about 5 minutes or until onions are softened but not browned.
If using fresh clams: Add the clams and 1 cup of water to the pot and turn the heat to high. Cover and cook, opening the lid every once in a while to stir the clams, until they begin to open, which should take about 3 minutes. As the clams open, remove them with tongs into to a large bowl, keeping as much juice in the pot as possible and keeping the lid shut as much as possible. After 8 minutes, discard any clams that have not yet begun to open. Roughly chop the clam meat and put it into a separate bowl with any of their juices. Add the milk and bay leaves to the pot, and add the cubed potatoes. Bring to a boil, then reduce the heat and simmer for about 20 minutes or until the potatoes are very tender and starting to break down. Add salt and pepper to taste.
If using canned or thawed clams: Stir the bottled clam juice and the milk and bay leaves into the pot and add the cubed potatoes. Bring to a boil, then reduce the heat and simmer for about 20 minutes or until the potatoes are very tender and starting to break down. Add salt and pepper to taste.
Add the chopped clams to the pot. Add the cream if you are using it, bring to a simmer and cook for two or three minutes (one minute for canned clams). Serve immediately. (I like it with a pat of butter melting on the top, but that’s just me.)