Add all-purpose flour, baking soda, and fine sea salt to medium mixing bowl. Whisk to combine. Set aside.
Add unsalted butter and creamy peanut butter to stand mixer. Using paddle attachment, beat 1 minute on medium speed.
Add light brown sugar and granulated sugar to stand mixer. Beat on medium speed for 2 minutes. Scrape down sides of bowl, if necessary.
Add egg and vanilla bean paste to stand mixer. Beat 30 seconds on low to incorporate.
Remove bowl from stand mixer. Add flour mixture to stand mixer bowl. Fold in with large spatula. Avoid over mixing.
Add peanut butter baking chips and dark chocolate chunks to cookie dough. Fold in using large spatula.
Cover bowl with plastic and chill 1 hour, or up to 3 days.
Preheat oven to 350 degrees F. Line 2 cookie sheets with parchment paper.
Scoop dough using cookie or ice cream scoop (about 3 tablespoons per cookie). Drop cookie dough onto prepared cookie sheets (6 cookies per sheet).
Press cookies down slightly.
Bake cookies in preheated oven for 10 to 12 minutes, or until cookies are golden along the edges, and set in the center.
Remove cookie sheets from oven and cool on wire racks.
Store leftover cookies for several days in an airtight container at room temperature. Freeze baked cookies for up to 1 month in a freezer proof zip-lock bag.