In a heatproof bowl, melt the butter in the microwave until it’s almost but not fully melted (about 1 minute at 100% power - if the butter was very cold you might need another 30-45 seconds).
Add the sugars and the vanilla and salt and whisk very vigorously, until the mixture starts to turn cohesive and shiny.
Add the peanut butter and whisk to combine.
Add the egg and whisk very well.
Fold in the oat flour, baking powder and soda and stir until there’s no visible flour bits.
Set the bowl in the fridge, uncovered for one hour. If you need to leave it longer, cover with plastic wrap to seal.
Preheat the oven to 350 F. Line two baking sheets with parchment paper.
Scoop the dough into 1.5 - 2 tablespoons of dough per cookie, leaving at least an inch diameter of space around each cookie as they will spread.
Bake for 10-12 minutes, until the edges are slightly golden and the cookies have puffed up and cracked.
Store cookies in an airtight container at room temperature.