Preheat oven to 350 degrees F (175 degrees C). Line cookie sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt; set aside.
In a large bowl, beat together the peanut butter, granulated sugar, and light brown sugar with an electric mixer on medium speed until light and fluffy, about 2 minutes.
Beat in the egg and vanilla until combined, about 1 minute.
Beat in the flour mixture until just combined.
Drop tablespoonfuls of cookie dough onto the prepared cookie sheets, about 2 inches apart.
Bake for 10 to 12 minutes, or until golden brown. Cool for 5 minutes before transferring to a wire rack to cool completely.
Interesting Facts
Peanut butter cookies were first developed in the United States in the late 1800s.
The cookies are often served with a glass of cold milk.
Peanut butter cookies are popular for bake sales and other fundraisers.