Preheat the oven to 350 and line a few baking sheets with parchment paper.
In the bowl of a stand mixer with the paddle, cream the butter, pb, both sugars and vanilla until light and fluffy, about 5 minutes. Scrape down the bowl occasionally to recombine the ingredients. Add the egg and mix again for another minute or two.
In a bowl, whisk the flour, baking powder, baking soda, cornstarch and salt until well combined. Add the mixture to the mixer and turn on low and mix just until it is almost mixed. Turn off the mixer and remove the bowl and finish the mixing by hand to prevent making your dough tough.
Divide the dough into 8 equal size pieces. You can eyeball this or use a digital scale. Roll them in your hands to make an circle and place on the two parchment lined sheets leaving ample room between the balls.
Press on them gently to flatten to about 2/3 of an inch thick. Freeze the cookie sheets for 15-30 minutes to make sure the dough is well set up and cold.
Bake in the oven for 10-13 minutes (check at the early time and watch them). You want them to look just very slightly under baked since they will continue to cook slightly on the cookie sheets when removed from the oven and you don't want overbaked cookies. Let cool on cookie sheets for a few minutes and then move to a cooling rack to cool completely before frosting.