In a large microwave-safe bowl, microwave 1 and 1/2 cups high-quality chopped chocolate or chocolate chips in bursts of 15 seconds, stirring between each burst for 15 seconds. Be very careful to slowly heat the chocolate and stir it frequently so it doesn't seize when other ingredients are added.
Stir in 1/2 cup Nutella until smooth and set aside.
In another bowl, combine cocoa powder and very hot water. Whisk until completely combined. Allow to slightly cool. (Both the melted chocolate mixture and this cocoa powder mixture should be about the same temperature.)
Gradually add the cocoa powder mixture to the chocolate mixture while beating with a hand mixer until completely smooth. It might look like it's not going to come together, but keep mixing-- it will come together!
Take 2 cups of cold heavy whipping cream (you'll whip the last cup later) and whip in a stand mixer until it reaches soft peaks. While whipping, add in the vanilla extract and 1/4 cup powdered sugar. Add half of the whipped cream to the chocolate mixture and fold in gently.
Take this mixture and add it all to the rest of the whipped cream. Gently fold until completely combined. The cream may seem a bit thin or even watery. Cover and place in the fridge to firm up for 1 hour. With a spatula, gently fold the cream again after chilling.
Fill a bowl with the whole milk. Separate the Oreos (No need to remove or separate the creme filling.) and dunk the halved cookies in the milk (no need to soak; just a dip). Place the cookie on the bottom of a 9x12-inch pan. Repeat with each halved Oreo, forming a single layer of cookie halves on the bottom of the pan. Once the cookies are all in an even layer, spread half of the chocolate cream over the Oreo layer.
Repeat the Oreo layer and the chocolate cream layer, using the rest of the chocolate cream. Add one last layer of dunked and halved Oreos.
In the stand mixture, whip the remaining 1 cup whipped cream with the remaining 2 tablespoons powdered sugar. Whip until you reach soft peaks. Spread evenly over the top of the Oreos. Crush up (with your hands) 2-3 leftover cookies to decorate the top of the cake. Cover and refrigerate for at least 8 hours and preferably overnight.
When ready to serve, remove from fridge and cut into squares. Serve and return any leftovers promptly to the fridge. Icebox cake lasts up to 1 week in the fridge. Unfortunately, this cake doesn't freeze and thaw well.