Preheat your oven to 350°F (175°C).
Start by sifting together the flour and baking powder, ensuring they are well combined.
In a stand mixer equipped with a paddle attachment, cream the butter and both sugars until light and fluffy. If desired, you can also add 1/4 to 1/2 teaspoon of sea salt at this stage.
Incorporate the peanut butter into the butter-sugar mixture, mixing until fully blended.
Add the egg and vanilla extract, mixing until the batter is smooth and creamy.
Gradually add the flour mixture to the wet ingredients, beating until everything is well incorporated and a dough forms.
Roll the dough into one-inch balls and place them on a baking sheet lined with parchment paper.
Using a fork, gently flatten each dough ball, creating a criss-cross pattern on top.
Bake the cookies for approximately 10 minutes, or until the edges are lightly golden.
Allow the cookies to cool completely on the baking sheet. This step is crucial as the cookies will continue to set and firm up before they can be transferred.