Using a handheld or stand mixer fitted with a paddle attachment, beat the butter on high speed until smooth and creamy, about 2 minutes.
Turn speed to low and slowly add 3 cups of powdered sugar, cocoa powder, and salt. Beat until well combined, about 2 minutes.
Increase mixer to medium speed and add vanilla and cream. Turn mixer to high speed and beat for 1 minute. Depending on thickness, you may need to add up to 1/2 cup additional powdered sugar.