Place sugar, whites, and salt in a heatproof mixer bowl set over a pot of simmering water. Whisk until sugar dissolves and mixture registers 160 degrees on a candy thermometer.

Attach bowl to mixer. Whisk on medium speed for 5 minutes. Increase speed to medium-high, and whisk until stiff, glossy peaks form, about 6 minutes. Reduce speed to medium, and add butter, 1 piece at a time, whisking well after each addition. Whisk in vanilla. Use immediately, or cover, and refrigerate for up to 3 days. (Bring to room temperature, and beat on low speed until smooth before using.)