Prepare a baking sheet by lining it with parchment paper or a silicone baking mat. Set aside.
In a heavy-bottomed saucepan, combine the granulated sugar, light corn syrup, salt, and cayenne pepper. Stir to combine.
Cook the mixture over medium heat without stirring until it reaches a temperature of 300°F (hard crack stage) on the candy thermometer.
While the sugar mixture is cooking, prepare the jalapeños. Remove the seeds and stem, then finely chop the peppers.
Once the sugar mixture reaches 300°F, quickly stir in the peanuts, chopped jalapeños, butter, and vanilla extract. Stir well to combine.
Immediately pour the mixture onto the prepared baking sheet and spread it out using a wooden spoon or silicone spatula.
Allow the brittle to cool completely at room temperature, which will take about 30 minutes.
Once cooled, break the brittle into pieces using your hands or a knife.
Store in an airtight container at room temperature for up to two weeks.