Line two cookie sheets with lightly buttered aluminum foil.
Combine the sugar, corn syrup, and water in a heavy saucepan. Cook over medium heat stirring constantly until the sugar is dissolved. Then continue cooking, stirring occasionally, until the mixture reaches 285 degrees or when a small amount dropped in cold water separates into hard but not brittle threads.
Add the peanuts and the butter.
Cook over medium heat, stirring constantly, to 300 degrees or until a small amount dropped in cold water separates into hard brittle threads.
Remove from heat. Quickly stir in the baking soda and the vanilla. The mixture will foam up.
Place the mixture onto the prepared cookie sheets. Spread out evenly as thin as possible with a metal spatula.
When completely cool, invert the pan and peel off the foil.
Break into serving size pieces and store at room temperature.