Step 1Heat the oven to 350 degrees. Spread the pistachios on a baking sheet and toast until lightly browned, about 9 to 10 minutes. Allow to cool on a rack.
Step 2Line a jellyroll pan with a silicone baking mat. (Or butter a jellyroll pan.) Have another jellyroll pan and baking mat ready if using the baking mats.
Step 3Mix together the sugar, water, light corn syrup and butter in a large, heavy saucepan and bring to a boil over medium heat, stirring just until the butter is incorporated and the sugar crystals are dissolved. Remove the spoon and do not stir again. Keep a small bowl of ice water and a pastry brush handy to brush down the sides of the pot as any sugar crystals start to form (this prevents the sugar from crystallizing and producing a grainy brittle). Simmer until the mixture turns a rich amber color, 12 to 14 minutes. Keep a close watch as the sugar will begin to turn amber quickly. Remove the pan from the heat. (It probably will not color evenly, but do not worry as the next step will mix it thoroughly).
Step 4Quickly mix in the baking soda, salt, vanilla and pistachios and pour the mixture onto the baking mat-lined pan. Flatten the mixture with the other baking mat to make a thin layer of brittle. (Or, if using the buttered jellyroll pan, use a buttered, offset spatula to quickly spread the mixture about 1/4-inch thick.) The mixture will be very hot and you may need to wear a kitchen mitt as you press on top of the mat to smooth the layer of brittle. Place the other jellyroll pan on top of the mat and press very hard to form an even layer. Lift off the pan and peel up the top mat. Place the bottom jellyroll pan with the brittle on a rack to cool thoroughly. When cool, break into pieces and store in a parchment-lined airtight tin.