Preheat the oven to 350°F. Line baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, granulated sugar, and brown sugar until light and fluffy, about 2 to 3 minutes.
Add the eggs, one at a time, mixing well after each addition. Add the vanilla extract and mix until combined.
In a medium bowl, whisk together the flour, baking soda, baking powder, and kosher salt.
Gradually add the dry ingredients to the butter mixture, mixing on low speed until just combined. Do not overmix.
Fold in the chopped Oreo cookies and peanut butter chips until evenly distributed throughout the dough.
Using a 2-tablespoon cookie scoop, scoop the dough onto the prepared baking sheets, spacing the cookies about 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are lightly golden and the centers still look slightly underbaked.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.