Melt the butter in a large saucepan over medium heat. Stir in the brown sugar and granulated sugar.
Continue stirring for 3 to 4 minutes, or until the sugar starts to bubble. Stir in the peanut butter, vanilla extract and salt. Continue mixing until smooth.
Using a rubber spatula, fold in the oats. Mix until all of the oats are evenly coated in the peanut butter mixture.
Line a baking sheet with parchment paper. Use a 2 inch cookie scoop to scoop 16 cookies onto the sheet. Transfer to the fridge for 30 minutes to allow the cookies to set.