Preheat the oven to 350 degrees F. Spread the nuts on a baking tray and toast for 8 to 10 minutes, turning the nuts after 5 minutes. Cool and then coarsely chop. Set aside.
Place the sugar in a medium deep saucepan. Add the corn syrup and water, and over medium heat, bring to a boil. Boil until a layer of bubbles forms on top, 3 to 4 minutes. Cover the pan with aluminum foil and continue to boil 5 minutes longer.
Remove the foil, add the butter, and stir with a wooden spoon until the butter is melted. Cook over medium heat until a candy thermometer registers 300 degrees F, about 30 minutes, stirring occasionally. Immediately stir in the salt, baking soda, and reserved nuts.
Meanwhile, coat with vegetable oil or spray a 12 by 17-inch half sheet pan. Spread the nut mixture over the prepared pan, spreading it as thin as possible with a long, metal spatula. When cool, run a clean, dry towel over the top to absorb some of the oil.
Cut or break the brittle into desired pieces.
Recipe courtesy of Mary Bergin and Judy Gethers, Spago Desserts, Random House 1994