Preheat the oven to 350 °F. Prepare a large cookie sheet by lining with a silicone mat.
Cream together butter and sugar in a large bowl. Add egg and then peanut butter and mix until well combined. Add vanilla, baking soda and salt and combine. Finally, add the oat flour and mix until fully incorporated.
Measure out the granulated sugar into a shallow bowl.
Scoop the dough into 1.5-2 tablespoon balls and roll each in the sugar until coated. Place on your prepared baking sheet and lightly squish down so they are about ½ inch/1 cm thick.
Bake for 8-9 minutes until the edges are just set. The centers will still be very soft.
Remove from the oven and use the back of a spoon to lightly flatten the tops and then let cool on the baking sheet for 10 minutes. Use a spatula to move the cookies to a wire rack to cool completely.