Grease an 8x8-inch baking dish and set it aside.

In a large saucepan, bring the granulated sugar and milk to a boil over medium heat, stirring constantly.

Once the mixture reaches a boil, continue cooking and stirring until it reaches the soft ball stage, which is around 235-240°F (112-115°C).

You can test this by dropping a small amount of the mixture into a glass of cold water.

If it forms a soft ball that flattens when removed from the water, it's ready.

Remove the saucepan from the heat and stir in the vanilla extract and peanut butter until smooth and creamy.

Quickly pour the mixture into the greased baking dish and spread it out evenly.

Let the fudge cool and set at room temperature for about 2 hours, or until firm.

Once set, cut the fudge into small squares and serve.