In a large bowl, sift the powdered sugar. Then add the dutch-processed cocoa powder (not the black cocoa powder) and set it aside.
Beat the room-temperature butter on medium-high (4-6) for about 6-7 minutes or until the butter is lighter in color and the consistency of mayonnaise. Scrape down the bowl occasionally with a rubber spatula.
Next, lower the mixer speed to low (1) scoop the sifted powdered sugar into the bowl a bit at a time.
When you have about half of the powdered sugar, add half of the milk.
Then add the remaining powdered sugar and the rest of the milk.
Add the vanilla.
Add the black cocoa powder and the food coloring. On low, mix until it is incorpoarated.
Turn the mixer to medium speed (4-6) and beat for at least two minutes.
The frosting will not be super black at this point. Cover the bowl with plastic wrap and keep overnight on the counter or the fridge. Within 24 hours, you should see it a dark black color. If it is still not black, you can add a tablespoon more of the black cocoa powder or stir it and wait an hour or so. It will continue to darkener the longer it sits.