In the bowl of a stand mixer with a paddle attachment (or using a large bowl and a hand mixer), mix the softened butter on medium-high speed until it is light and fluffy, which takes about 5 minutes.
Reduce the mixer speed to low. Gradually add the sifted powdered sugar, one cup at a time, mixing until just combined before adding the next batch.
Scrape down the sides and bottom of the bowl as needed to ensure everything is incorporated.
Sift the cocoa powder and espresso powder into the bowl.
Mix on low speed until the powders are incorporated.
Mix in the vanilla and salt.
Pour in the heavy cream, one tablespoon at a time, mixing until you reach your desired consistency.
Increase the mixer speed to medium-high and beat for 3 to 5 minutes, until the buttercream is light and fluffy.
