Take 8 Oreos and coarsely chop them into small bite-sized pieces. Measure to get 1 cup of cookie pieces and set aside. For the frosting, take 6 Oreos and blend in a blender or food processor until you have fine crumbs. Set aside.
Cut butter straight from the fridge into small cubes. In a large bowl, or stand mixer fitted with whisk attachment, add in the cubed butter and brown sugar. Beat with a hand mixer until completely combined and ultra creamy, about 3–4 minutes.
Add the egg and vanilla, and beat until combined. Then, mix in the cornstarch, baking soda, salt, and cocoa powder, beating until just combined and scraping down the sides as needed. Next, add the cake flour and regular flour, mixing again until just combined—be careful not to overmix. Gently fold in the mini and regular chocolate chips, along with the coarsely chopped Oreos, using a spatula. Cover the bowl tightly and refrigerate for 45 minutes to 2 hours.
After chilling, remove the bowl from the fridge and form cookie dough balls. Each ball should be just over 4 ounces. You should get 6 equal-sized balls from the dough. Place rolled balls on a parchment-paper-lined sheet pan or plate and return to the fridge or freezer to chill for 15 more minutes.
Meanwhile, preheat the oven to 325℉. Line an extra-large sheet pan with a silicone baking mat or parchment paper. Add 3 cookie dough balls to the pan, leaving plenty of space in between each cookie. Bake for 13–18 minutes, erring on the side of slightly under-baking. Remove from the oven and immediately press the edges of the cookie inwards with the back of a metal spatula to get the perfect round bakery-style cookie. Let cookies stand on the pan for 10–15 minutes before removing them to a cooling rack. Allow cookies to cool and finish firming up here. Repeat process with the last 3 cookies.
In a large bowl, or stand mixer fitted with whisk attachment, beat the butter until smooth, creamy, and light, about 3–4 minutes. Add in 1 cup of powdered sugar and beat until combined. Beat in the remaining 1 cup powdered sugar, vanilla, and salt, and then just enough heavy cream to get the frosting to a pipeable consistency, about 3 tablespoons. Stir in the crushed Oreo crumbs until integrated. Transfer to a piping bag fitted with an open star tip and generously pipe frosting on each cookie. Alternatively, spread on frosting with a knife.
For the perfect finishing touch, add a couple of mini Oreo cookies, halved regular-sized Oreos, or some coarse Oreo crumbs (just break with your hands) to the top of the cookies.
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Notes
Note 1: Dutch-process cocoa powder offers a more robust flavor, do not replace with regular cocoa powder.Note 2: Cake flour gives the cookies a fluffy, tender crumb and keeps them soft and chewy; combine it with all-purpose flour for the best texture, and avoid substitutes or homemade versions.Note 3: Flour needs to be spooned into the measuring cup and leveled with the back of a butter knife to ensure you are using the correct amount. Video visual here.STORAGE: Don't frost cookies you plan on storing. Keep the frosting in an airtight container in the fridge and the cookies at room temperature in an airtight container, frosting just before serving.