Line two baking sheets with parchment paper or wax paper and set aside.
In a medium saucepan, combine sugar, milk, butter, and cocoa powder. Bring to a rolling boil over medium heat, stirring constantly.
Once boiling, let mixture boil for exactly 1 minute without stirring, then remove from heat immediately.
Quickly stir in peanut butter, vanilla extract, and salt until peanut butter is completely melted and mixture is smooth.
Add oats and stir vigorously until all oats are evenly coated with the chocolate mixture.
Working quickly, drop heaping tablespoons of the mixture onto prepared baking sheets, spacing them about 1 inch apart.
Let cookies cool at room temperature for 30 minutes until firm and set. For faster setting, you can refrigerate them for 15 minutes.
Store cookies in an airtight container at room temperature for up to a week, or refrigerate for up to 2 weeks. These also freeze beautifully for up to 3 months!