Preheat oven to 350 degrees.
In a bowl, combine the flour, baking powder and baking soda; use a whisk to combine, set aside.
Using a mixer with a paddle attachment, cream together the butter and peanut butter.
Add sugars and beat at medium speed for 4 minutes, scraping down bowl twice.
At low speed, add eggs and vanilla.
Add flour mixture and beat at low speed until well mixed, frequently scraping down bowl.
Add oats, and mix well.
Using a small scoop, place balls of dough on parchment-lined baking sheets.
Bake until cookies have spread and turned very light golden brown, about 10 – 12 minutes.
Remove from oven and set aside to cool and firm up, 10 to 15 minutes. Transfer to a rack to cool completely before filling.