Heat a 4 to 6 quart heavy pot over low heat and add the diced salt pork. Once it has rendered a few tablespoons of fat, increase the heat to medium and cook until the pork is a crisp golden brown. Use a slotted spoon to transfer the cracklings to a small ovenproof dish; reserve.
Add the butter, onions, savory or thyme, and bay leaves to the fat in the pot and cook over medium heat, stirring occasionally with a wooden spoon, until the onions have softened but not browned, about 8 minutes.
Add the potatoes and stock. If the stock doesn't cover the potatoes, add a little water. Turn up the heat and bring to a boil. Cover the pot and boil the potatoes vigorously until they are soft on the outside but still firm in the center, about 10 minutes. If the stock hasn't thickened slightly, smash a few of the potato slices against the side of the pot and cook for 1 to 2 minutes longer.
Reduce the heat to low and season assertively with salt and pepper (you want to almost over season at this point in order to avoid having to stir once the fish is added). Add the fish fillets and cook over a low heat until the fish is almost done, 5 minutes. Remove the pot from the heat and allow the chowder to sit for 10 minutes (the fish will finish cooking during this time).
Gently stir in the cream and taste for salt and pepper. If you are not serving the chowder within the hour, let it cool a bit, then refrigerate (only cover the chowder after it has chilled completely). Otherwise, let it sit for up to an hour at room temperature, allowing the flavors to meld.
When ready to serve, reheat the chowder over a low heat; don't let it boil. Warm the cracklings in a low oven (220 degrees F) for a few minutes.
Use a slotted spoon to mound the chunks of fish, the onions, and potatoes in the center of large soup plates or shallow bowls, ladle the creamy broth around and scatter the cracklings over top. Finish each serving with a sprinkling of chopped parsley and minced chives.
Strong Fish Stock:
Yield:about 2 quarts
Melt the butter in a heavy 7 to 8-quart stockpot over medium heat. Add the onions, celery, carrots, bay leaves, parsley, thyme, and peppercorns and cook, stirring frequently with a wooden spoon, until the vegetables become very soft without browning, about 8 minutes.
Place the fish head on the vegetables and stack the fish frames evenly on top. Pour in the wine, cover the pot tightly and let the bones sweat until they have turned completely white, 10 to 15 minutes.
Add enough very hot or boiling water (approximately 2 quarts) to just barely cover the bones. Give the mixture a gentle stir and allow the brew to come to a simmer. Simmer for 10 minutes, uncovered, carefully skimming off any white foam that comes to the surface (try to leave the herbs, spices and vegetables in the pot).
Remove the pot from the stove, stir the stock again and allow it to steep undisturbed for 10 minutes. Ladle through a fine-mesh strainer and season lightly with salt. If you are not going to be using the stock within the hour, chill it as quickly as possible.
Cover the stock after it is thoroughly chilled (it will have a light jellied consistency) and keep refrigerated for up to 3 days, or freeze for up to 2 months.