Spray a 9-inch square baking pan with nonstick cooking spray, line with aluminum foil, and spray again.
Place sugar, corn syrup, water, and butter in a medium saucepan. Place over medium-high heat and stir until sugar is dissolved. Stop stirring at this point and remove the spoon.
Wash down any sugar crystals that develop on the sides of the pan with a pastry brush dipped in water.
Heat the mixture until a candy thermometer registers 285 degrees Fahrenheit. This will take approximately 10 minutes.
While the sugar mixture is boiling, in a medium heatproof bowl, combined peanut butter, peanuts, and salt. Microwave the mixture for approximately 30 seconds. Stir the mixture and microwave for another 20-30 seconds until the peanut butter is liquified and hot.
In a small bowl, whisk baking soda and vanilla extract.
Add baking soda mixture to the mixture in the saucepan, whisking to combine. Mixture will foam up.
Remove from heat and immediately add hot peanut butter, stirring with a metal or wooden spoon to combine quickly.
Immediately pour mixture into the foil-lined pan and smooth the top. Allow to cool completely for several hours at room temperature.
Remove the square of candy from the pan, peel off the foil, and place candy onto a cutting board. Cut into small squares as desired and store in an air-tight container in a single layer, separated by wax paper. Candy can be stored at room temperature for at least 2 weeks.