In a large mixing bowl, add cocoa and whisk to break up any lumps.
Add butter to cocoa and cream together with an electric mixer until well combined and smooth.
Add the sugar, 1 cup at a time, alternating with 1 tablespoon of milk, mixing until combined before each addition.
After all the sugar and cream are combined, turn mixer on high speed for about 1 minute.
Add vanilla and espresso powder until well combined.
If frosting looks too dry add more cream ½ tablespoon at a time; if too wet add more powdered sugar until desired consistency.