Brush a 9-by-13-inch rimmed baking sheet with butter, and oil an offset spatula; set aside. I used my oven tray covered in baking paper.
Put sugar, corn syrup, and salt in a medium saucepan with ¼ cup cold water. Bring to a boil over medium-high heat, stirring until sugar has dissolved. Wash down sides of the pan with a wet pastry brush to prevent crystals from forming.
Cook, swirling the pan occasionally, until the mixture registers 238C/460F degrees on a candy thermometer (soft-ball stage). To test this, drop a little mixture into a glass of cold water and then take it out with a spoon. If it's solid but soft (I hope that makes sense!), it's ready.
Stir in nuts, and continue to cook, stirring often so that the nuts do not burn, until the mixture is medium amber in color, 10 to 15 minutes. Carefully stir in vanilla and baking soda (the mixture will foam up). I took mine off the heat before I did this.
Pour onto prepared baking sheet, and using oiled spatula, quickly spread into a ½-inch-thick layer. Let cool completely.
Break brittle into pieces if desired; store in an airtight container at room temperature up to 1 month.