Preheat the oven to 350°F and line cookie sheets with parchment paper.
In a large bowl, cream together butter, peanut butter, and sugars until light and fluffy. Beat in eggs and stir in vanilla.
In another bowl, mix together flour, baking soda, baking powder, zest, and salt.
Stir dry ingredients into butter mixture until well-incorporated. Scrape the bottom and sides as needed to incorporate loose flour.
Form dough into 1-inch balls and put on cookie sheets, flattening with a fork or the bottom of a cup. If dough is too sticky to easily form into balls, refrigerate for 1 hour.
Bake for approximately 10 minutes. Let cool on cookie sheet 2 minutes before moving to a rack to finish cooling.