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.