In the bowl of a stand mixer with paddle attachment or in a large bowl with a hand mixer, cream together butter both sugars until light and fluffy, about 2-3 minutes.
Mix in eggs one at a time. Mix in vanilla extract.
In a separate large bowl, whisk together flour, baking soda, baking powder, and salt.
Mix the dry ingredients into the wet ingredients until just combined, taking care not to over-mix. Fold in chocolate chips and Oreo pieces until just combined.
Put dough in fridge to chill for 60 minutes (or longer).
When cookie dough is almost done chilling, preheat oven to 350 degrees and line a baking sheet with parchment paper.
Scoop about 3 tablespoon of cookie dough (I use a #20 cookie scoop) onto the prepared baking sheets about 1 ½ inches apart. Top with more chocolate chips and Oreo pieces if you want.
Bake cookies for 12-14 minutes, until cookies are just turning golden around the edges, but are still soft. Let cookies cool in the pan for a couple minutes before moving to a wire rack to cool completely.