Butter two heavy baking sheets (or line them with foil, then butter them). Stir together sugar, water, and corn syrups in a (very, very) large saucepan and heat over medium heat until sugar dissolves. Increase heat to high and boil until the temperature on your candy thermometer reaches 260F (about 40 minutes).
Turn heat to medium-low. Mix in peanuts and butter and cook until temperature reaches 295F, stirring constantly (about 15 minutes). Add baking soda and vanilla; mixture will foam up vigorously and you will be worried it will overflow. Pour immediately onto prepared baking sheets. Spread out as thinly as possible.
Cool until hard. Break into pieces. Store in airtight containers at room temperature. Should keep for about a month.