Preheat oven to 350. Line baking sheets with parchment paper.
In a small bowl, combine the flour, baking soda, baking powder and salt. Set aside.
In a large bowl, beat together butter, granulated sugar and brown sugar until light and fluffy. Stir in the peanut butter, egg and vanilla. Gradually stir in the flour mixture until combined.
Roll into 1 inch balls and place on the prepared baking sheets.
Bake for 10 minutes, then remove from oven. Use a rounded measuring spoon to make a small indentation in the middle of each cookie. Return cookies to the oven for another 6 to 7 minutes or until golden edges. After removing from oven make the spoon indentation again. Transfer to cooking rack and let cool completely.