Line a baking sheet or tray with parchment paper or a silicone mat. Lightly grease a spatula for spreading later.
If desired, lightly toast the pecans until fragrant, then set them aside.
In a heavy saucepan, combine the sugar, corn syrup, and water. Cook over medium heat, stirring gently until the sugar dissolves. Once the mixture begins to boil, reduce stirring and let it cook until it reaches the hard crack stage (300–310°F / 149–154°C).
Stir in the butter, salt, and pecans. Mix carefully until the pecans are coated well.
Remove the pan from the heat. Immediately stir in the baking soda and vanilla extract, if using. The mixture will foam quickly.
Pour the hot brittle onto the prepared baking sheet. Spread it gently into a thin layer.
Let the brittle cool completely at room temperature.
Once fully cooled, break it into pieces and store in an airtight container.