Begin by lining a baking dish or square pan with parchment paper or aluminum foil, ensuring that it covers the bottom and sides. This will make it easier to remove the fudge once it's set.
In a medium-sized saucepan, combine the granulated sugar and whole milk. Place the saucepan over medium heat and stir continuously until the mixture comes to a gentle boil.
Reduce the heat to low and let the mixture simmer for about 3 minutes, continuing to stir consistently.
Remove the saucepan from the heat and add the creamy peanut butter and pure vanilla extract. Stir vigorously until the mixture becomes smooth and creamy.
Gradually sift the confectioners' sugar into the saucepan, stirring continuously to ensure that it incorporates well.
Once all the ingredients are fully combined and the mixture is smooth, quickly pour it into the lined baking dish, spreading it evenly using a spatula or the back of a spoon.
Allow the fudge to cool at room temperature for about 1-2 hours until it is completely set.
Once set, remove the fudge from the baking dish by lifting the edges of the parchment paper or aluminum foil. Place it on a cutting board and cut it into bite-sized squares or rectangles.
Serve and enjoy the irresistible Alton Brown Peanut Butter Fudge!