Line two baking sheets with parchment paper and set them aside.
In a medium saucepan, over medium heat, combine sugar, milk, butter, salt, and cocoa. Stir until the butter has melted. Bring the mixture to a full boil and allow to boil for 1½ minutes, stirring constantly. Immediately remove the pan from the heat.
Add the peanut butter and vanilla and stir until the peanut butter is melted and fully incorporated.
Add the oats and stir to combine. Allow the mixture to cool for 10 to 15 minutes, stirring a few times. This allows the oats to absorb some of the moisture so the cookies don't spread out too much.
Using a 1.5 tablespoon cookie scoop or a spoon, drop cookies onto the prepared baking sheets. If desired, flatten the cookies slightly with the bottom of a glass or measuring cup.
Allow to cool completely. The cookies will firm up as they cool. *To cool quicker, place the pan of cookies in the refrigerator for 30 minutes. Store in an air-tight container in the refrigerator for up to one week.