Preheat the oven to 350ºF. Lightly spray two standard donut pans with nonstick cooking spray or melted coconut oil to avoid the donuts from sticking to the pan. Set aside.
In a large bowl, whisk together the butter, eggs, milk, and vanilla. Stir until well combined. To the same bowl, add the cocoa powder, flour, sugar, baking powder, baking soda, and salt. Mix until just combined. Set aside.
Transfer the batter into a ziplock plastic bag or piping bag, cut a hole in one corner, and pipe the batter into the donut molds, filling each one about 3/4 full.
Bake for 10-12 minutes, or until a toothpick inserted into the center comes out clean. Let cool for 5 minutes before flipping the pans upside down over a rack to remove the doughnuts.
In the meantime, whisk together the cream cheese, sugar, milk, and vanilla until smooth and combined. The mixture will be very thick.
Dip the tops of each donut in the icing or use the back of a spoon to spread a thick layer. Top each donut with crushed Oreo cookies before allowing them to set for 10-20 minutes, or until the icing is slightly hardened. Serve with a tall glass of milk and enjoy!