Line two baking sheets with parchment paper or wax paper and set aside.
In a large saucepan, combine sugar, milk, butter, and cocoa powder. Bring to a rolling boil over medium heat, stirring constantly.
Once boiling, continue to boil for exactly 1 minute without stirring, then remove from heat immediately.
Quickly stir in peanut butter and vanilla extract until smooth and well combined.
Add the gluten-free oats and salt, stirring until everything is evenly coated.
Working quickly, drop spoonfuls of the mixture onto the prepared baking sheets, using about 2 tablespoons per cookie.
Allow cookies to cool at room temperature for 20-30 minutes until completely set and firm to the touch.
Store in an airtight container at room temperature for up to 5 days.