Ready to use, hydrated cod can be found at most fish shops. However, if you choose to buy dry salted cod, soak it in a large bowl of cold water for 2 to 3 days, changing the water 3 to 4 times a day. This will rehydrate the cod and ensure that it is not too salty.
Cut the cod into 2 by 2-inch pieces. Lightly dredge the cod in flour, shaking off any excess, and set aside.
In a large saucepan, heat 1 cup of the extra-virgin olive oil. Make sure the oil is hot before adding the cod, otherwise the cod will absorb the excess oil. Cook until golden brown on both sides.
In another saucepan, heat the remaining 1/4 cup oil. Add the garlic, chili peppers, and capers, and let cook for a few minutes. Add the plum tomatoes along with the juices and crush some of the plum tomatoes with a wooden spoon. Add the oregano, season with salt, and cook for 5 minutes.
Put the cod in the sauce and cook for an additional 2 minutes. Sprinkle the dish with fresh parsley and serve warm or at room temperature.