Combine the butter and cocoa powder in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a handheld electric mixer). Mix on low speed until combined. Add the vanilla and salt. Continue to mix on low speed, adding the sugar a cup at a time and alternating with additions of the milk. Increase the speed to medium-high and mix until smooth. Use immediately, or refrigerate in an airtight container up to 3 days. Allow to come to room temperature and mix on medium-high until smooth.