Martha's Swiss Meringue Buttercream

Bring a saucepan filled with about 2 inches of water to a simmer. Meanwhile, combine sugar, egg whites, and salt in a large heatproof mixing bowl. Set bowl over (not in) pan of simmering water and whisk until whites are warm to the touch and sugar has dissolved, 2 to 3 minutes. (Test by rubbing between your fingers; mixture should feel smooth.)

Attach bowl to mixer fitted with the whisk attachment; beat on medium-high speed until stiff, glossy peaks form and mixture has cooled completely, about 12 minutes.

Reduce speed to medium-low; add butter, 2 tablespoons at a time, beating to incorporate fully after each addition. (Don't worry if buttercream appears curdled at this point; it will become perfectly smooth again with continued beating.) Beat in vanilla.

Switch to paddle attachment and beat on lowest speed to remove air bubbles, 3 to 5 minutes. If using buttercream the same day, cover bowl with plastic wrap and let stand at room temperature until ready to use.

If not using the same day, transfer buttercream to an airtight container and refrigerate up to 3 days. Before using, bring to room temperature, then beat with paddle attachment on lowest speed until smooth and pliable, about 10 minutes.