Butter two large baking sheets generously and set aside. Have a candy thermometer ready.
In a heavy 3-quart saucepan, combine sugar, corn syrup, and water. Cook over medium heat, stirring constantly, until sugar dissolves.
Bring to a boil and clip candy thermometer to side of pan. Continue cooking without stirring until mixture reaches 280°F.
Stir in peanuts and continue cooking, stirring frequently, until temperature reaches 305°F (hard crack stage) and mixture is golden brown.
Immediately remove from heat; quickly stir in butter, baking soda, vanilla, and salt. Mixture will foam.
Working quickly, pour onto prepared baking sheets and spread thin with a buttered spatula or wooden spoon.
Let cool completely, then break into pieces. Store in an airtight container with wax paper between layers.