Make your Homemade Cookies and Cream first so it has time to harden in the freezer. Line a small baking tray with parchment paper, set aside. Roughly chop the Oreos, you want to have more smaller pieces than larger (think cookies and cream!), set aside. Microwave white chocolate chips in a microwave safe bowl in 30 second intervals, mixing in between until chocolate is smooth. Pour melted chocolate onto the prepared tray and smooth with an off set spatula and/or spoon until you have an even layer. Sprinkle chopped Oreos all over white chocolate and gently press down, making sure the Oreo pieces stick to the white chocolate. Place in freezer while you start the cookies.
Preheat the oven to 410 degrees and line two cookie sheet pans with parchment paper. With a stand mixer fitted with a paddle attachment, whip the butter until it's fluffy. Add in the light brown sugar and granulated white sugar and cream together until the mixture is light in color.
Add in both eggs and vanilla, mix until combined, scraping down the sides as needed to ensure its all combined.
Add in the all purpose flour, cake flour, salt, baking soda, and cornstarch. Set the mixer on lowest speed and mix until JUST COMBINED, leaving a few streaks of flour behind. Add in semi sweet and dark chocolate. Remove chocolate from freezer and break up into pieces (either by hand or placing in a bag and hitting with something hard like a glass), add it in with the dough and continue on lowest speed until JUST combined (5-10 seconds).
You can make these into 8 large cookies, or 16 medium size cookies (large cookies measure out ~165g / medium cookies measure out ~100g). Scoop the dough using a large cookie scooper, place the dough on a sheet pan lined with parchment paper. These cookies won’t spread a lot, but I wouldn’t overcrowd them on the cookie sheet. Bake for 14-18 minutes (see note). Leave them on the baking pan for 15 minutes to continue cooking, then transfer to a cooling rack.
*Optional Drizzle* Once the cookies are cool, melt together the white chocolate and leftover cream from the crushed cookies in 30 second intervals in the microwave until smooth. Drizzle over cooled cookies.