1. Whisk together egg whites and sugar in a heatproof mixing bowl over a pan of simmering water until sugar has dissolved, about 5 min. Test by rubbing the mixture between your fingers -- you shouldn't feel any sugar crystals.
2. Transfer bowl to the mixer stand with whisk attachment or use a handheld mixer and beat on high until it cools and stiff peaks form, 10 to 12 min.
3. Reduce speed to medium high and add butter a little at a time. (Buttercream may curdle but will become smooth as you continue to beat it.) Add vanilla.
4. Use within a few hours or refrigerate up to a week. Before using, bring to room temperature and beat on low until smooth. Makes 10 cups.