Line an 8×8 inch baking pan with parchment paper or lightly grease it with butter.
Heat the Sugar and Milk:
In a medium saucepan, combine the granulated sugar and milk. Cook over medium heat, stirring constantly, until the sugar is dissolved.
Boil the Mixture:
Bring the mixture to a boil, and let it cook without stirring until it reaches the soft-ball stage, which is about 234°F (112°C) on a candy thermometer. This should take around 5-7 minutes.
Add the Peanut Butter and Vanilla:
Remove the saucepan from the heat. Stir in the peanut butter, vanilla extract, and butter until the mixture is smooth and well combined.
Pour and Set:
Pour the mixture into the prepared baking pan, spreading it evenly with a spatula.
Cool and Cut:
Allow the fudge to cool at room temperature for about 2 hours, or until it is set.