In a medium bowl, whisk flour, baking soda, and salt together. Set aside.
Add butter and sugars into bowl of a stand mixer. Cream until mixture is smooth, about 3 minutes. Add egg and vanilla and beat until combined. Add in flour mixture 1/2 cup at a time until just combined.
Add in chocolate chips and 1 1/2 cups of Oreo pieces and fold in. Prepare two baking sheets with parchment paper or silicone mats.
Scoop about 1 1/2 tablespoons of dough per cookie onto baking sheets about 2 inches apart. Add remaining Oreo pieces to the top of each cookie. Refrigerate dough until thoroughly chilled, at least 2 hours.
Once dough is chilled, preheat oven to 350 degrees. Bake cookies in preheated oven for 9-10 minutes, or until edges get golden brown. Remove from oven and cool completely on baking sheet.