Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a small bowl, combine the all-purpose flour, baking powder, and salt. Set it aside.
In a large bowl, beat softened butter, creamy peanut butter, packed brown sugar, and granulated sugar until the mixture is smooth and creamy.
Incorporate the egg and vanilla extract into the butter mixture, mixing until fully blended.
Gradually mix in the flour mixture until just combined. Be careful not to overmix.
Form the dough into 1-inch balls and arrange them on the prepared baking sheet. Use a fork to lightly press each ball, forming a criss-cross pattern on top.
Bake for approximately 8 to 12 minutes, or until the edges are lightly browned. Let the cookies cool on the baking sheet for 5 minutes before moving them to a wire rack.