Combine the sugar and egg whites in the bowl of an electric mixer. Set the bowl over a small pot of simmering water and, whisking constantly, heat until the sugar has dissolved and the mixture is hot, taking care not to cook the eggs.

Place the bowl back in the mixer fitted with a whip attachment. Whip on high speed for about 10 minutes, until the mixture forms a stiff meringue and the bottom of the bowl comes to room temperature. Replace the whisk with the paddle attachment.

With the mixer on low speed, begin adding butter a few cubes at a time, beating until they are incorporated before adding more. Once all the butter has been added, increase speed to medium and beat until fluffy.

Reduce mixer speed to low and beat in the vanilla. Scrape down the sides and bottom of the bowl, then beat on medium speed until the buttercream is smooth and creamy.

The buttercream can be used immediately, stored in an airtight container at room temperature for up to 2 days or refrigerated for up to 10 days.

Variations:

Chocolate: Add ½ cup (4 ounces) melted and cooled semisweet chocolate in a steady stream while mixing on low speed.

Mocha: Add ¼ cup of cold strong coffee and ¼ cup melted and cooled semisweet chocolate, each in a steady stream with the mixer on low speed.

Lemon: Reduce the amount of vanilla extract to 2 tablespoons. Add the zest of 2 lemons and 3 tablespoons of pure lemon extract.

Fruit: Add ½ cup seedless fruit (raspberry, strawberry, etc.) puree.