Set the oven to preheat at 350°F. Combine the flour with the baking powder by sifting them together, then whisk lightly to ensure even distribution. In the bowl of a stand mixer equipped with a paddle attachment, cream together the butter, granulated sugar, and brown sugar until light and fluffy; if desired, incorporate 1/4–1/2 teaspoon of sea salt for added depth. Add the peanut butter and continue mixing until fully blended. Introduce the egg along with the vanilla extract, mixing until uniform. Gradually add the flour mixture and beat on low until just incorporated. Form the dough into one-inch balls and arrange them on a parchment-lined baking sheet. Gently press each ball with a fork, creating a crosshatch pattern. Bake for approximately 10 minutes or until the edges are set but the centers remain soft. Allow the cookies to rest on the baking sheet until completely cool and firm enough to transfer.