Preheat your oven to 350°F (175°C).
Line a baking sheet with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large mixing bowl, use an electric mixer to cream together the unsalted butter, creamy peanut butter, brown sugar, and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, mixing well after each addition. Then, add the pure vanilla extract and mix until fully incorporated.
Gradually add the dry ingredient mixture to the wet ingredients. Mix until just combined, being careful not to overmix.
Gently fold in the chopped Oreo cookies and chocolate chips until evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, leaving space between each cookie. Press additional Oreo pieces on top if desired and sprinkle with flaky sea salt.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a cooling rack to cool completely.