Butter a large, heavy baking sheet. Stir first four ingredients in large, heavy saucepan over medium heat until sugar dissolves. Increase heat to high and boil without stirring until candy thermometer registers 260 degrees, about 20 minutes.
Reduce heat to medium-low. Mix in peanuts and butter and cook until thermometer registers 295 degrees, stirring constantly, about 7 minutes.
Add baking soda, vanilla, and cayenne if desired and stir briskly. Immediately pour out onto prepared baking sheet. Spread out brittle as thinly as possible. Let stand until cold and hard.
Break brittle into pieces. Store in airtight containers at room temperature.