Combine the granulated sugar and milk in a large saucepan over medium-high heat.
Stir it just until the sugar is incorporated into the milk, then leave it alone.
When the mixture comes to a boil (as soon as you start seeing consistent bubbles), stop stirring and start a timer for about 2 and a half minutes.
After 2 and a half minutes, remove the pot from the heat.
Quickly add the salt, vanilla and peanut butter.
Beat the mixture with a wooden spoon just until the peanut butter is melted and mixed throughout, a minute or two.
Pour the fudge mixture into the pan and smooth the top.
Put the pan on a cooling rack to set and cool completely. It usually takes a couple of hours.
Cut into 16 pieces and store in an airtight container.