Heat a 2 to 3-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, leaving the fat in the pot, and reserve until later.
Add the butter, onions, savory or thyme, and bay leaf to the pot and saute, stirring occasionally with a wooden spoon, for about 8 minutes, until the onions are softened but not browned.
Add the potatoes and stock. If the stock doesn't cover the potatoes, add just enough water to cover them. Turn up the heat and bring to a boil, cover, and cook the potatoes vigorously for about 10 minutes, until they are soft on the outside but still firm in the center. If the stock hasn't thickened lightly, smash a few of the potato slices against the side of the pot and cook for 1 or 2 minutes longer to release their starch. Reduce the heat to low and season assertively with salt and pepper (you want to almost over season the chowder at this point to avoid having to stir it much once the fish is added). Add the fish fillets and cook over low heat for 5 minutes, then 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; cover the chowder after it has chilled completely. Otherwise, let is sit for up to 1 hour at room temperature, allowing the flavors to meld.
When ready to serve, reheat the chowder over low heat; don't let it boil. Warm the cracklings in a low oven (200 degrees) 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, and ladle the creamy broth around. Scatter the cracklings over the individual servings and finish each with a sprinkling of chopped parsley and minced chives.