Whisk sugar and egg whites in a large heatproof bowl set over a pan of simmering water until sugar is dissolved and mixture registers 140 degrees.on an instant read thermometer, 2 to 3 minutes.
Fit an electric mixer with the whisk attachment, and beat the egg-white mixture on high speed until it holds stiff (but not dry) peaks and mixture is fluffy and cooled, about 10 minutes.
Reduce speed to medium-low, and add butter several tablespoons at a time, beating well after each addition (meringue will deflate slightly as butter is added). Add vanilla, beat until frosting comes together, 3 to 5 minutes. Beat on the lowest speed until air bubbles diminish, about 2 minutes. Stir with a rubber spatula until frosting is smooth.
You can refrigerate the buttercream in an airtight container up to one week, or freeze it up to one month. Before using, bring it to room temperature and stir with a rubber spatula to smooth.