In a medium heatproof bowl, beat egg yolks with a hand mixer fitted with the beater attachments at medium-high speed until pale yellow and slightly thickened, 3 to 4 minutes.

In a small saucepan, stir together sugar and 3 tablespoons (45 grams) water over medium heat until sugar dissolves. Using a pastry brush dipped in water, brush sides of pan to prevent sugar granules from crystallizing. Increase heat to high, and bring to a boil. (Do not stir.) Cook until an instant-read thermometer registers 240°F (116°C).

With mixer on low speed, slowly pour hot sugar syrup into egg yolk mixture in a slow, steady stream, being careful not to hit sides of bowl or mixer attachments; scrape sides of bowl. Increase mixer speed to high, and beat until bottom of bowl feels cool to the touch and mixture is very thick and very pale yellow, 4 to 5 minutes. Add butter, 1 tablespoon (14 grams) at a time, beating at medium speed until combined after each addition. (Mixture will look broken at times, but keep beating and it will come back together.)

In a small bowl, stir together espresso and remaining 1¾ teaspoons (9 grams) water. Add espresso mixture and salt to buttercream, and beat at low speed until combined, stopping to scrape sides of bowl. Use immediately.