Get ready by lining a rimmed baking sheet with parchment paper, and measuring all the ingredients. When the brittle reaches the "hard crack" stage of candy making, you will need to work quickly, so it's essential to have everything measured and ready to go.
In a heavy-bottomed stock pot, combine the sugar, corn syrup, water, vanilla, and salt. Clip a candy thermometer (preferably digital) to the side of the pot, so that the tip of the thermometer is submerged in the syrupy liquid.
Set the pot on the stove, and turn the burner to medium heat or just below medium. You don't want to cook the sugar too quickly or aggressively, or you'll risk burning it.
Cook the sugar, stirring occasionally with a wooden spoon, until the temperature reaches between 240-245 F.
Stir in the softened butter and the peanuts; you can expect the temperature to drop slightly from the addition of ingredients.
Continue to cook the candy, stirring occasionally, until the temperature reaches between 290-300 F (hard crack stage for 5,000 feet elevation). It may take up to 30 minutes to reach this point from the start, but don't be tempted to walk away. You need to stay near the stove, because although the temperature may start off rising slowly, it can rise very quickly towards the end of the cooking process.
Remove from the heat and stir in the baking soda, which will make the candy bubble up a bit.
Working quickly, immediately pour the hot candy onto the parchment lined baking sheet, using the wooden spoon to scrape as much of the candy out of the pot as you can. Spread the candy out with the spoon so it reaches the edges of the pan.
If you like, immediately sprinkle the top of the brittle with a few extra peanuts and a pinch of flaky salt.
Let the candy cool completely at room temperature for about two hours.
Use the pointed end of a sharp knife to pierce the hard candy, causing it to break into jagged chunks.