Make sure all ingredients are ready and measured out before starting. Some steps require quick action, so this will help the process.
Preheat the oven to 170°F.
Grease a 10x15 jelly roll pan or cookie sheet with at least 1-inch tall sides. Set aside.
In a large pot over medium heat, bring sugar, corn syrup, salt, and water to a boil. Stir until the sugar is dissolved. When the liquid looks clear, that indicates the sugar has dissolved.
While the mixture is heating up, add the jelly roll pan to the preheated oven so it can warm up.
Clip the candy thermometer to the side of the pot, making sure the tip sits in the candy mixture without touching the bottom of the pan. When the temperature reads 250°F, stir in 1 cup of peanuts. Cook on medium-low heat at a steady boil until the temperature reaches the hard crack stage of 300°F (takes about 10-13 minutes). If you don't have a thermometer, drop a small amount of the candy mixture into a bowl of cold water, if it separates into hard and brittle threads, it's ready.
Once the mixture reaches 300°F, this is the fast part. Remove from heat and immediately stir in butter, baking soda, and vanilla. When the baking soda is stirred in, the mixture will foam, lighten in color, and become full of tiny bubbles. That is exactly what you want.
Working quickly, pour back and forth onto the cookie sheet. Using oven mitts, move the pan around until the mixture spreads out. The recipe will not fill the whole pan, do not spread with a knife or spatula. **Be careful with the hot sugar. The candy mixture is extremely hot at 300°F. Use oven mitts and keep kids away from the stove while pouring and spreading the brittle.
After pouring/spreading, allow it to sit at room temperature for 10 minutes to cool. Then place in the refrigerator for another 20-30 minutes.