Preheat oven to 350°F (175°C).
In a mixing bowl, cream together the peanut butter, butter, granulated sugar, and brown sugar until smooth.
Beat in the egg.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until combined.
Roll dough into 1-inch balls and place on a baking sheet. Flatten each ball with a fork, making a criss-cross pattern.
Bake for 10 minutes, or until edges are lightly browned.
Allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.