Melt butter in a Dutch oven or large pot. Add oysters. If you are using fresh oysters, cook them until they firm up (the edges will start to ripple). If you are using canned oysters, they are already cooked and do not need to be cooked again. Be sure to add all the juices with the oysters.
Add the half-and-half slowly, then the milk. If you are adding dried parsley, add it now. Cook over low heat. Stir occasionally, so it does not burn or curdle. Add a dash or two of onion salt. Add more onion salt and pepper, to taste.
Crumble in Saltine crackers and cook a little longer. Taste again to make sure you have enough seasoning.
Once the soup is heated through, take it off the burner. Reheat before serving! Even on low, it can get too hot, and the soup will curdle. Serve with extra Saltine or oyster crackers.