1. Combine sugar, egg whites, and salt in bowl of stand mixer; place bowl over pan of simmering water. Whisking gently but constantly, heat mixture until slightly thickened, foamy, and registers 150°F on instant-read thermometer, 2 to 3 minutes.

2. Place bowl in stand mixer fitted with whisk attachment. Beat mixture on medium speed until consistency of shaving cream and slightly cooled, 1 to 2 minutes. Add butter, 1 piece at a time, until smooth and creamy. (Frosting may look curdled after half of butter has been added; it will smooth with additional butter.) Once all butter is added, add vanilla; mix until combined. Increase speed to medium-high and beat until light, fluffy, and thoroughly combined, about 30 seconds, scraping beater and sides of bowl with rubber spatula as necessary.

3. If final frosting seems too thick, warm mixer bowl briefly over pan of simmering water. Place bowl back on mixer and beat on medium-high speed until creamy.

Makes about 2 1/4 cups