Place the butter into a large mixing bowl. Using a hand mixer, beat the butter until light and fluffy.
Add the ground espresso and freshly pulled espresso shots. Beat again on high until completely combined with the butter, scraping down the sides as needed.
Add 2 cups of the powdered sugar and beat on high until well combined. Add the remaining powdered sugar, salt, and heavy cream. Beat again on high until light and fluffy, about 1 minute, scraping the sides down as needed.