Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.
In a large bowl, cream together the butter, granulated sugar, brown sugar, and peanut butter until light and fluffy.
Beat in the egg until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt. Gradually stir the dry ingredients into the wet ingredients until just blended.
Roll dough into 1-inch balls and place 2 inches apart on the prepared baking sheets. Flatten each ball with a fork, making a crisscross pattern.
Bake for 9 to 10 minutes or until edges are lightly browned.
Cool on baking sheets for 5 minutes before transferring to wire racks to cool completely.
Notes
Store cookies in an airtight container at room temperature for up to 5 days.