In a small bowl, stir together espresso powder and 1½ teaspoons (7.5 grams) water until dissolved and well combined.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter until smooth and creamy, about 2 minutes, stopping to scrape sides of bowl. With mixer on low speed, gradually add confectioners’ sugar, beating until combined. Add espresso mixture, vanilla, and salt; beat at medium speed until smooth and fluffy, about 2 minutes.