1. Starting a day ahead, place the cod in a glass, enameled or stainless-steel pan or bowl, cover it with cold water, and soak for at least 12 hours, changing the water 3 or 4 times.
2. Drain the cod, rinse under cold running water, place it in a saucepan, and add enough fresh water to cover the fish by 1 inch. Bring to a boil over high heat. (Taste the water. If it seems excessively salty, drain, cover the cod with fresh water, and bring to a boil again.)
3. Reduce the heat to low and simmer uncovered for about 20 minutes, or until the fish flakes easily when prodded gently with a fork. Drain thoroughly. With a small knife, remove and discard any skin and bones and separate the fish into fine flakes. Set aside.
4. Drop the pumpkin or squash into enough lightly salted boiling water to cover it completely, and boil briskly for about 20 minutes, or until tender. Drain in a sieve or colander, return the cubes to the pan and slide the pan back and forth over moderate heat for 10 to 15 seconds, until the pumpkin or squash is completely dry.
5. Puree the squash through a ricer set over a deep bowl, or mash it thoroughly with a fork. Beating vigorously with a large spoon, add the softened butter, the cod flakes, eggs and a few grindings of pepper, and continue to beat until the mixture is smooth.
6. Taste and add salt as needed. The mixture should be thick enough to hold its shape solidly in the spoon. If it is too thin, beat in up to 1 cup bread crumbs, a tablespoon or two at a time.
7. To form each salt fish ball, flour your hands lightly, scoop up about 1 tablespoon of the fish mixture and shape it into a round ball about 1inch in diameter. Dip the ball in the remaining 1 cup of crumbs. As they are shaped and coated, place the balls side by side on wax paper.
8. In a heavy 10- to 12-inch skillet, heat the oil or lard over moderate heat until a light haze forms above it. Fry the balls, 5 or 6 at a time, for about 3 to 4 minutes, turning them with a spatula and regulating the heat so they color richly and evenly without burning. As they brown, transfer them to paper towels to drain.
9. Serve the salt fish balls while they are still warm as a first course or as an accompaniment to drinks.
