Use this creamy frosting to decorate our Flag Layer Cake.
Place sugar and egg whites in a heatproof mixer bowl; set over (not in) a pan of gently simmering water and whisk until sugar is dissolved and egg whites are hot to the touch, 2 to 3 minutes. (Test by rubbing mixture between your fingers; it should feel completely smooth.)
Transfer bowl to stand mixer with whisk attachment and beat on medium speed 5 minutes. Increase speed to medium-high and beat until stiff, glossy peaks form and meringue has cooled (test by feeling bottom of bowl), about 7 minutes.
Reduce speed to medium-low and add butter, several tablespoons at a time; beat after each addition until incorporated. (Don't worry if buttercream appears curdled after all of butter has been added; it will become smooth again with continued beating.) Add vanilla and beat just until combined.
Switch to paddle attachment and beat on lowest speed until any air pockets are eliminated, about 5 minutes. If you'll be using the buttercream within several hours, cover the bowl with plastic wrap and set aside at room temperature in a cool environment. Otherwise, transfer it to an airtight container and store in the refrigerator for up to three days. Before using, bring buttercream back to room temperature, and beat it on the lowest speed with the paddle attachment until smooth, about 5 minutes.