Preheat your oven to 350°F. Line a baking sheet with parchment paper.
Sift the flour and baking powder together into a bowl. Whisk to combine and set aside.
In a stand mixer fitted with a paddle attachment, cream the butter and both sugars together until light and fluffy. If your peanut butter is not very salty, you can add 1/4 to 1/2 teaspoon of sea salt at this step.
Add the peanut butter and mix until fully combined.
Mix in the egg and vanilla extract. Once blended, add the flour mixture and beat just until everything is incorporated. Do not overmix.
Roll the dough into 1-inch balls and place them on the prepared baking sheet. Leave a little space between each one.
Flatten each cookie gently with a fork, making a criss-cross pattern on top.
Bake for about 10 minutes. The cookies will look almost done but still soft in the center.
Leave the cookies on the baking sheet to cool completely. They will continue to set from the heat of the pan. Once cooled, they will be firm enough to move and ready to enjoy.