Generously butter a large baking sheet (or two smaller ones) and set aside. Have all ingredients measured and ready before you start cooking.
In a large heavy-bottomed saucepan, combine sugar, corn syrup, and water. Cook over medium heat, stirring constantly, until sugar dissolves completely.
Stir in peanuts and continue cooking, stirring frequently, until a candy thermometer reads 300°F (hard crack stage), about 15-20 minutes. The mixture will turn a golden amber color.
Immediately remove from heat and quickly stir in butter, vanilla, baking soda, and salt. The mixture will foam up—this is normal!
Working quickly, pour the hot mixture onto the prepared baking sheet and spread it thin using a buttered spatula or wooden spoon.
Allow to cool completely at room temperature for about 1 hour. Once hardened, break into pieces by tapping with the back of a spoon or hitting with a mallet. Store in an airtight container for up to 3 weeks.