Step 1Butter a jellyroll pan and set it aside.
Step 2Combine the sugar, corn syrup and water in a heavy 2 1/2-quart saucepan. Clip a candy thermometer to the pan so it reaches the ingredients. Place the pan over medium-high heat; stir until the sugar dissolves. When the syrup comes to a boil, stir in the butter. Keep the mixture at a low boil, stirring frequently, as the syrup becomes golden and thick, about 20 minutes.
Step 3Continue cooking the syrup until the thermometer registers 280 degrees (soft-crack stage). Stir in the peanuts, which will lower the temperature. Stir constantly until the thermometer reaches 305 degrees (hard-crack stage). Remove the pan from the heat; quickly stir in the baking soda and vanilla.
Step 4Immediately pour the hot mixture (carefully) onto the prepared pan. Use the back of a wooden spoon to spread it out to the edges of the pan. When cool, lift the brittle from the pan and break it into bite-size pieces.