In a large bowl, using an electric hand mixer, beat your cream cheese and butter until light and creamy. Add in the sugar and beat until combined. Beat in the flour in 3 parts. Don't over mix. Fold in the Oreo pieces. Cover the bowl with plastic wrap and refrigerate for 45 minutes.
Preheat your oven to 350°F. Form your dough into balls and place on a baking sheet lined with parchment paper. With you three fingers, flatten them out. Bake for 10 minutes and then bump up the oven to 375°F and bake for another 2-3 minutes. Edges should be just starting to turn golden and cookies should look underdone in the center. Allow to sit on the baking sheet to cool for 10 minutes.