Place the salt cod in a large pot of water and let soak for 24 to 36 hours, depending on how dry the fish is, until softened. Change the water at least twice during the process.
Drain the fish and cut into 2-inch chunks.
In a large pot, layer the potatoes, onions, and cod. Add the tomatoes, pimientos, garlic, bay leaves, two-thirds of the parsley, the chiles, peppercorns, and olive oil. Gently simmer for 30 minutes, then reduce the heat to low and cook for 45 minutes. Shake the pot every now and then, but do not stir.
Gently ladle the stew into six bowls, sprinkle with the remaining parsley, and serve with plenty of crusty bread.