Add all-purpose flour, baking powder, baking soda, and sea salt to small bowl. Whisk to combine and set aside.
Add unsalted butter and peanut butter to stand mixer. Using the paddle attachment, beat on medium low until smooth and creamy.
Add granulated sugar and light brown sugar to stand mixer. Beat on medium until well combined, about 2 minutes.
Add egg and vanilla bean paste. Beat on low just until incorporated.
Remove bowl from stand mixer. Fold or stir in flour mixture until no streaks of flour remain.
Cover the bowl with plastic wrap and refrigerate cookie dough for 60 minutes.
Preheat oven to 350 degrees F. Line 2 cookie sheets with parchment paper.
Using an ice cream or large cookie scoop, portion 12 cookies from chilled dough onto the two prepared cookie sheets, 6 cookies per sheet, evenly spaced. Press the cookies down slightly.
Use a fork to make crosshatch lines across the top of each cookie, if desired.
Bake cookies in preheated oven for 15 minutes, or until cookies are light brown on the edges and slightly soft in the center.
Remove cookie sheets from oven and cool completely on wire rack.
Store cookies in an airtight container for up to 5 days.