In a medium bowl set over a pan of about 2 inches of gently boiling water that is not touching the bowl, add egg white and sugar.
Constantly whisk the sugar and egg whites for about 4-5 minutes until the sugar has dissolved completely or an instant read thermometer reads 160 degrees.
Remove the bowl and place into a stand mixer or use a hand mixer and mix on low speed gradually increasing to medium high speed for 10-15 minutes until a thick and glossy meringue forms.
The bowl and the meringue should be cool to the touch so if it is not, continue mixing until it has cooled.
Add the butter cubes, one at a time, mixing well after each addition until all the butter is incorporated. *See notes or blog post for troubleshooting if your frosting is runny or curdled.
Add the salt and espresso powder and beat until the espresso powder has dissolved completely.