In a heavy 2-quart saucepan over medium-high heat stir together the sugar, corn syrup, and water. Constantly stir the mixture until it reaches 285 degrees F on a candy thermometer.
Take the pan off the heat and stir in the peanuts and butter. Place the pan back on the heat and stir constantly until the mixture reaches 295 degrees F.
Moving quickly, take the pan off the heat and stir in the vanilla and baking soda. Pour the mixture into your prepared cookie sheet and let it sit until set, about 30 minutes.
Break the brittle into pieces and store in an airtight Ziploc bag or container.