Preheat oven to 350℉/175℃. Line 2 large baking trays.
In a large bowl, or the bowl of a stand mixer, combine the butter and both sugars on a medium/high speed for about 3 minutes. Add in the egg, peanut butter and vanilla and combine again.
Add in the flour, baking powder and baking soda. Mix until all combined to a thick cookie dough.
Place tablespoon sized balls of dough on the lined baking sheets, about 2 inches apart.
Press indents into the cookies in a criss cross pattern. Bake 10 minutes, until just golden.
Remove and let cool before serving!