Remove the unsalted butter from the refrigerator at least 1 hour before you plan to make the frosting. The butter should be soft enough to leave an indentation when pressed, but not melted or shiny.
Place a fine mesh sifter over a bowl and combine the powdered sugar and unsweetened cocoa powder. Sift together to remove lumps and ensure they are fully combined.
Place the softened butter in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed for 3 to 4 full minutes, scraping down the sides and bottom once, until the butter is pale, fluffy, and almost ivory colored.
Turn the mixer to low speed and add the sifted cocoa and powdered sugar mixture in three additions, beating for about 20-30 seconds after each. Once all dry ingredients are added, increase speed to medium and beat for 1 minute until mostly combined.
With the mixer running on low, pour in 3 tablespoons of heavy cream, vanilla extract, and salt. Mix for 30 seconds to incorporate, then increase to medium-high and beat for 2-3 minutes, scraping down the bowl once, until light and fluffy.
Check the consistency. If too thick, add the remaining 1 tablespoon of cream and beat another 30 seconds. If too soft, add 2-3 tablespoons of sifted powdered sugar and beat briefly.
Use immediately for the best piping results. For spreading, use an offset spatula in smooth, sweeping strokes. For piping, transfer to a piping bag with a desired tip.