Prepare a Baking Sheet. Line a baking sheet with parchment paper and set it aside. You'll pour the hot brittle mixture onto this sheet later.
Combine Sugar, Corn Syrup, Water, and Salt. In a heavy-bottomed saucepan, combine the sugar, corn syrup, water, and salt. Stir them together over medium-high heat until the sugar dissolves. Once the mixture begins to boil, insert a candy thermometer.
Cook to 300°F (Hard Crack Stage). Without stirring, let the mixture cook until it reaches 300°F (Hard Crack Stage) on the candy thermometer. This will take about 8-10 minutes. Be patient and keep an eye on the temperature.
Add Peanuts and Butter. Once the mixture reaches 300°F, stir in the roasted peanuts and butter. Continue cooking, stirring constantly, until the temperature reaches 310°F (Hard Crack Stage). This should take another 3-5 minutes. The mixture will turn a lovely golden color.
Remove from Heat and Add Vanilla and Baking Soda. Remove the saucepan from the heat and quickly stir in the vanilla extract and baking soda. Be cautious as the mixture will bubble up when you add these ingredients. Mix until everything is well combined.
Pour onto Baking Sheet. Immediately pour the hot peanut brittle mixture onto the prepared baking sheet. Use a heat-resistant spatula or the back of a spoon to spread it out into an even layer. Allow it to cool and harden completely.
Break into Pieces Once the peanut brittle has cooled and hardened (usually within 30 minutes to an hour), break it into bite-sized pieces using your hands or a mallet.
Store. Store the peanut brittle in an airtight container at room temperature. It should stay fresh for several weeks.