Put egg whites and sugar into the heatproof bowl of an electric mixer set over a pan of simmering water. Cook, whisking constantly, until sugar has dissolved and mixture is warm to the touch (about 160 degrees).
Attach the bowl to the mixer fitted with the whisk attachment. Beat on high speed until stiff (but not dry) peaks form. Continue beating until mixture is fluffy and cooled, about 6 minutes.
Switch to the paddle attachment. With mixer on medium-low speed, add butter, several tablespoons at a time, mixing well after each addition. (If the frosting appears to separate after all the butter has been added, beat on medium-high speed until smooth again, 3 to 5 minutes more.) Reduce speed to low; mix to eliminate any air bubbles, about 2 minutes. Stir with a rubber spatula until frosting is smooth.