Line a baking sheet with parchment paper and set it aside. Arrange the peanuts, butter, baking soda, and vanilla so they are measured and ready for immediate use. In a medium-sized saucepan, combine sugar and water, stirring to blend thoroughly, then incorporate the corn syrup. Set the pan over medium heat, taking care not to increase the heat, and stir occasionally until the mixture reaches a gentle boil. Fasten a candy thermometer to the side of the pot, ensuring the bulb is immersed in the syrup but not in contact with the bottom. Continue cooking, stirring intermittently, until the temperature rises to 250°F (121°C). Stir in the peanuts and maintain constant stirring as the thermometer climbs to 300°F (149°C). Once the desired temperature is reached, withdraw the pan from heat and immediately mix in the butter, baking soda, and vanilla; the mixture will foam and alter in consistency. Promptly pour the hot brittle onto the prepared pan and, using a knife or spoon, carefully spread it into an even layer. Allow the candy to cool undisturbed for at least 30 minutes, then break it into pieces. Store in an airtight container once completely cooled.