Render diced salt pork in a heavy pot over low heat until it releases a few tablespoons of fat. Increase heat, add butter and onion, and saute until onion is tender but not browned. Add parsnips, potatoes, and stock, and bring to a boil. Cook vigorously for about 10 minutes, or until vegetables are barely tender. Reduce heat to low.
Remove 2 cups of the chowder from the pot and puree in a food mill or processor, then return it to the chowder. Stir in the cream, and let chowder simmer slowly for another 5 minutes; broth should look silky-smooth. Remove from heat, and season with salt and pepper.
If not serving within the hour, let cool then refrigerate; cover after it has chilled completely. Otherwise, let it set at room temperature for up to an hour, allowing the flavors to meld. When ready to serve, reheat the chowder over low heat; don't let it boil. Garnish with minced chives, parsley or celery leaves.