In a large saucepan over high heat, combine the sugar, corn syrup and water. Bring to a boil and reduce the heat to medium-high. Cook undisturbed until a candy thermometer registers 260˚, about 20 minutes. Reduce the heat to medium-low and add the peanuts. Wait 5 seconds, then give the mixture a brief stir. Continue cooking, swirling the saucepan occasionally to prevent scorching, until the mixture turns deep golden brown, about 3 minutes.
Remove the saucepan from the heat and stir in the butter and vanilla. Add the baking soda (the mixture will foam) and stir until incorporated.
Pour the peanut mixture onto a rimmed baking sheet lined with a silicone mat or parchment paper, and spread into an even layer. Let the brittle stand until cool and hard, about 25 minutes. Break the peanut brittle into pieces and store in an airtight container at room temperature for up to a month.