Fit a stand mixer with the paddle attachment. Add the softened cream cheese and room-temperature salted butter to the mixer bowl. Beat on medium speed until the mixture is light and fluffy, stopping once or twice to scrape down the sides of the bowl.

Add the sugar and beat on medium speed until well combined and smooth.

With the mixer on low, add the all-purpose flour a small amount at a time, mixing just until the flour is incorporated. Do not overmix.

Transfer the dough to a mixing bowl (or leave in the mixer bowl) and fold in the broken Oreo pieces with a rubber spatula until evenly distributed.

Cover the bowl tightly with plastic wrap and refrigerate the dough for at least 45 minutes and up to 2 hours.

About 30 minutes before you plan to bake, preheat the oven to 350°F.

Line a large baking sheet with parchment paper.

Use a 2-tablespoon cookie scoop (or measure 2 tablespoons) to portion the chilled dough. Roll each portion into a round and place the rounds on the prepared baking sheet, spacing them about 2 inches apart. Lightly press each cookie to slightly flatten.

Bake in the preheated oven for 10–11 minutes, or until the edges are just beginning to turn golden. The centers will still be soft when removed.

Remove the baking sheet from the oven and let the cookies cool on the sheet for 10 minutes. Then transfer the cookies carefully to a cooling rack to cool completely.