Line a rimmed baking sheet with parchment and lightly grease it. Set a heatproof spatula nearby.
Warm the peanuts in a low oven for 5 minutes so they stay crisp when added.
Combine sugar, corn syrup, water, and salt in a heavy saucepan. Stir just to moisten the sugar.
Bring to a steady boil over medium heat without stirring. Clip on a candy thermometer.
Cook until the syrup reaches 250°F. Stir in the warmed peanuts carefully.
Continue cooking, stirring occasionally, until the mixture hits 300°F and turns deep golden.
Remove from heat. Quickly stir in the butter and vanilla until glossy.
Sprinkle in baking soda and stir briskly. The candy will foam and lighten.
Pour immediately onto the prepared pan. Tilt and gently spread thin with the spatula.
Cool completely, about 30 minutes. Break into pieces and store airtight.