Whisk the egg whites, sugar and salt in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water) until the mixture is warm and the sugar dissolves. Remove the bowl from the pan; let cool slightly.
Beat the egg white mixture in a stand mixer fitted with the whisk attachment (or with a hand mixer) on medium-high speed until stiff peaks form, 12 to 15 minutes. Beat in the butter a few pieces at a time, then continue beating until smooth. (Don't worry if the mixture looks separated at first-it will come together as you keep beating.)
Make sure that your butter is nice and soft (with no chill) or the buttercream may curdled when mixing.