Preheat oven to 350°F. In a medium bowl, whisk together flour and baking powder; set aside.

In a large bowl, beat peanut butter, sugar, and butter until smooth. Beat in egg. Gradually add flour mixture, beating to combine.

Pinch off dough by the tablespoon; roll into balls. Place 2 inches apart on parchment-lined baking sheets. Using a fork, press balls in a crisscross pattern, flattening to a 1/2-inch thickness.

Bake cookies, rotating halfway through, until lightly golden, 18 to 22 minutes. Cool cookies on a wire rack.