Preheat oven to 375°F and line 2 large baking sheets with parchment paper and set aside.
Chop up 12 of the Oreos and set them aside in a bowl. Chop up the remaining 6 Oreos and set them aside in a separate bowl.
18 Oreos
In a large bowl or stand mixer (highly recommend a stand mixer for this recipe) fitted with a paddle attachement, cream together the butter and sugar on medium speed for 2 minutes, scraping down the sides of the bowl halfway through.
1½ cups unsalted butter, 1 cup granulated sugar, 1½ cups light brown sugar
Add the eggs one at a time, mixing after each one just until the yolk is streaky throughout the dough. Add the vanilla extract and mix just for a couple of seconds.
2 large eggs, 1 teaspoon vanilla extract
In a medium mixing bowl, whisk together the flour, powdered milk, cornstarch, salt, and baking soda. With the mixing beating at low (stir) speed, slowly add the flour mixture. If you have a flour shield for your mixer, I recommend using this as this recipe creates a lot of dough. Increase to medium speed and mix just until combined then remove from the mixer and use a rubber spatula to mix up any loose flour from the bottom of the bowl into the dough.
4 cups all-purpose flour, 1 tablespoon powdered milk, 1 tablespoon cornstarch, 1½ teaspoons salt, 1 teaspoon baking soda
Add the 12 chopped Oreos, white chocolate chips, and mini chocolate chips and mix at low speed just until combined, be careful not to overmix. You can finish mixing with a rubber spatula or with your hands until the dough is fully combined and the chips are evenly incorporated.
12 ounces white chocolate chips, ¾ cups mini chocolate chips
Use a large cookie scoop to portion out the dough on the prepared baking sheets, leaving 5 inches between each (about 6 to 8 cookies will fit on a standard cookie sheet). For chewier cookies, gently use your hands to press the cookies dough until they're about 1-inch thick. For a softer, slightly underdone texture, leave the dough as is after scooping. Press the remaining Oreos and some additional chocolate chips (make sure to leave some white chocolate chips for drizzle later) into the top of the cookies.
Bake the cookies one cookie sheet at a time for 8 to 10 minutes, or until the edges are just turning light brown, the centers should still be very soft and look underdone. Remove from the oven and allow them to cool for 5 minutes on the pan before transferring them to a wire rack to cool completely. Then transfer the cooled cookies to parchment paper.
Melt the remaining white chocolate chips in a small bowl at 30-second intervals, stirring between each one, until completely melted. Transfer to a piping bag and cut off the tip and drizzle over the cooled cookies. Allow the chocolate to set.
12 ounces white chocolate chips