Line an 8-inch square baking pan with parchment paper.
Allow for a 2-inch overhang on all sides and lightly grease with nonstick cooking spray.
Combine the sugar, milk, and salt in a medium saucepan.
Cook over medium heat, stirring constantly until it comes to a boil.
Once it reaches a boil, set a timer and boil for exactly 3 minutes without stirring.
Remove from heat.
Add the peanut butter, butter, and vanilla extract.
Stir until completely melted and smooth.
Pour the mixture into the prepared pan and spread evenly.
Let the fudge cool completely at room temperature, about 2 hours.
Use the parchment paper as handles to lift the fudge from the pan.
Cut into 16 squares.