In a the bowl of a mixer fitter with a whipping attachment, whip the butter and cocoa.
Add the icing sugar and milk alternating in three stages. Whip at high speed till well blended and fluffy. Stop, scrape the side and continue mixing for a few minutes.
Slow down the mixer and add the whipping cream, vanilla, and espresso. Increase the speed to high and whip till well blended.
Recipe by Swine + Wine at https://www.swineandwine.ca/chocolate-butter-cream-frosting/