In a large bowl, cream together the butter, peanut butter, vanilla and sugars. Beat in the eggs until fully incorporated.
In a separate bowl, combine the flour, baking powder and baking soda. Slowly add it into the wet ingredients and mix until fully combined. Place the batter in the refrigerator for 1 hour.
Preheat the oven to 375˚F.
Roll into one inch balls and place on ungreased baking sheet. Flatten each ball with a fork, making a criss cross pattern.
Bake in the preheated oven for around 10 minutes, or until the cookies begin to brown.
Remove from oven, and place on wire racks to cool completely.