Prepare a 9-inch springform pan by lining the sides with parchment paper that sticks about an inch above the sides of the pan.
To make the mousse, beat the cream cheese and sugar for together in a large mixer bowl until smooth.
Add the milk and beat until smooth. Set cream cheese mixture aside and make whipped cream.
Whip the 2 1/2 cups of heavy whipping cream on high with a mixer until it begins to thicken. Add vanilla extract and powdered sugar and continue to whip on high until stiff peaks form.
Carefully fold 1/3 of the whipped cream into the cream cheesecake mixture until combined. Add the remaining whipped cream and fold mixtures together until well combined.
Divide the mousse into two bowls. You’ll want twice the amount in one bowl as the other. You should have about 2 1/3 cups in one bowl and the rest in another.
Add the cocoa powder and red food coloring to the bowl with the larger amount of mousse and combine.
Add the slightly cooled white chocolate to the smaller amount and combine.
Pour the milk for the cookie layers into a small bowl. Place a single layer of cookies into the bottom of the pan, dipping each into the milk before adding.
Top the cookies with half of the red velvet mousse and spread into an even layer.
Add another layer of cookies on top of the red velvet mixture, dipping each into the milk before adding.
Top the cookies with the white chocolate mousse and spread into an even layer.
Add another layer of cookies on top of the chocolate mixture, dipping each into the milk before adding.
Top the cookies with the remaining red velvet mousse and spread into an even layer.
Refrigerate cake until firm, 4-5 hours. Once firm, remove icebox cake from pan.
To make whipped cream for topping, whip heavy whipping cream on high until it begins to thicken. Add the powdered sugar and vanilla extract and continue to whip on high until stiff peaks form.
Spread a layer of whipped cream on top and then pipe the whipped cream around the top edge of the cake.
Refrigerate until ready to serve. Top with additional red velvet Oreo crumbs.