Spread the nuts on a baking tray and toast them in the oven until light golden, 6 to 8 minutes, turning the nuts after 4 minutes so they toast evenly. Remove them from the oven and let them cool to room temperature.
Put the sugar in a medium saucepan. Add the corn syrup and water turn stove to medium heat, stir once to mix, bring to a boil. Continue boiling, undisturbed, until a layer of bubbles forms on top, 3 to 4 minutes. Cover the pan with aluminum foil and continue to boil undisturbed for 5 minutes longer. I place a wooden spoon on top of the foil to keep down.
Remove the foil, add the butter, gently stir with a wooden spoon a few times. When the butter has melted and is combined with the sugar mixture -- and forms a soft boil add your candy thermometer continue cooking over medium heat, stirring occasionally, until a candy thermometer inserted into the mixture registers 300 degrees (150 C), about 12 - 15 minutes. Meanwhile, coat a 12-by-17-inch (30-by-43-cm) sheet pan with vegetable oil or spray it with nonstick cooking spray.
As soon as the sugar mixture reaches the desired temperature, immediately but carefully stir in the combined salt and baking soda, vanilla and Pistachios.
Using a long metal spatula, spread the nut mixture as thinly and evenly as possible over the prepared pan. Leave the brittle to cool to room temperature. The brittle will harden very quickly.
When the brittle is completely cooled and hardened, run a clean, dry towel over the brittle's surface to absorb some of the oil. Carefully cut or tap the brittle with a mallet to break it into irregular pieces. Store in one or more airtight containers at cool room temperature.