Before getting started, preheat your oven to 350°F (175°C).
Then, in a large mixing bowl, beat together the softened butter, granulated sugar, peanut butter, and brown sugar until the mixture becomes light and fluffy.
Stir in the egg and vanilla extract until evenly mixed.
In another mixing bowl, blend together the flour, baking powder, baking soda, and salt by whisking thoroughly.
Pour the dry ingredients into the wet mixture little by little, and stir gently until they're fully incorporated.
Using your hands, create 1-inch-sized balls from the dough and position them on a baking sheet lined with parchment paper, maintaining a distance of about 2 inches between every cookie.
Press lightly with a fork on each cookie to make a crosswise design.
Wait for the edges to become slightly golden, a process that takes between 10-12 minutes, and let the cookies rest for 5 minutes on the baking sheet before transferring them to a wire rack to cool down entirely.