Preheat your oven to 350°F. Spray the bottom and sides of an 8x8-inch square baking pan with cooking spray. Line the bottom and sides with parchment paper; spray the parchment with cooking spray. Set aside.

In a small saucepan over medium heat using a wooden spoon or a spatula, stir butter, cocoa powder, and chopped chocolate constantly until the mixture is melted and smooth, about 3 to 5 minutes. Remove from heat; set aside to cool slightly.

In a large bowl using a hand mixer or in the bowl of a stand mixer with the paddle attachment, beat both sugars and eggs together on medium-high speed for 3 to 4 minutes until the mixture is pale and thickened. Gently stir in vanilla extract, then stir in the cooled butter-chocolate mixture. Stir in flour and salt until the mixture is just combined. Stir in chocolate chips and half of the chopped Oreo cookies (about 1/2 cup) until just incorporated.

Pour batter into the prepared baking pan. Top evenly with remaining chopped Oreo cookies. Bake for 25 to 28 minutes or until a toothpick inserted near the center of the pan comes out clean or with moist crumbs clinging (do not overbake). Cool the brownies completely in the pan on a cooling rack.

Meanwhile, make the icing: In a small bowl, whisk together powdered sugar and milk until a smooth, easy-to-drizzle icing forms. Use a spoon or fork to drizzle icing over cooled brownies. Allow icing to set slightly.

Use the parchment paper to remove brownies from the baking pan. Using a sharp knife in a gentle sawing motion, cut the brownies into squares.