Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
In a large bowl, cream together butter, granulated sugar, and brown sugar until light and fluffy. Beat in peanut butter, egg, and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Roll dough into 1-inch balls and place on prepared baking sheets. Flatten slightly with a fork, making a crosshatch pattern.
Bake for 8-10 minutes, or until edges are lightly golden. Let cool on baking sheets for a few minutes before transferring to a wire rack to cool completely.
Notes
Enjoy these chewy peanut butter cookies with a glass of milk!