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.
Remove from heat immediately and quickly stir in butter, baking soda, vanilla, and salt. The mixture will foam up—this is normal!
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.