Place the butter, peanut butter, and both sugars in the bowl of an electric mixer and cream until light and fluffy, about 3-4 mminutes.
Beat in the egg and vanilla.
In a seperate bowl combine the flour, baking powder, baking soda and salt.
Add the flour mixture to the butter mixture and beat until combined. Next, fold in the chopped chocolate.
Preheat oven to 350 degrees and line 2 cookie sheets with parchment paper.
Roll the dough into 24 balls, they should be about 1 1/2 inch in diameter, and place them on the cookie sheets. Refrigerate the dough balls for about 15 minutes.
Bake the cookies for 15 minutes or until light golden brown. Place the cookie sheets on a rack to cool for about 10 minutes and then remove the cookies and place them directly on the rack to cool completely. Leaving the cookies on the pan to cool for 10 minutes is very important. Do not try and remove the cookies from the pan immediately after removing from the oven or they will become a gooey mess.