Preheat oven to 375°F.
In a large bowl, cream together the peanut butter, butter, granulated sugar, and brown sugar until well blended. Beat in the egg and vanilla.
In a separate bowl, combine the flour, baking powder, and salt; stir into creamed mixture.
Scoop dough into balls. (I used a 3-tablespoon scoop.) Place cookies 2 inches apart onto ungreased cookie sheets. Gently press each ball of dough with the bottom of a glass to slightly flatten. (Note: Dip the bottom of the glass in confectioners' sugar if glass is sticking to dough.)
Bake for 8 to 10 minutes in the preheated oven, or until edges are lightly browned. Do not overbake!
Cool completely on a cooling rack, about 45 minutes.