01 - Line two baking sheets with parchment paper and set aside.
02 - Combine butter, sugar, milk, and salt in a medium saucepan. Bring to a rolling boil over medium heat, stirring occasionally. Boil for exactly 1 minute.
03 - Remove saucepan from heat immediately. Stir in peanut butter and vanilla extract until mixture is completely smooth.
04 - Add quick-cooking oats to the saucepan and mix thoroughly until evenly coated.
05 - Drop heaping tablespoons of the mixture onto the prepared baking sheets. Flatten slightly using the back of a spoon.
06 - Allow cookies to stand at room temperature for at least 15 minutes, or until firm to the touch.