In medium glass or metal bowl, beat egg whites and sugar with whisk until blended. Set over pan of simmering water 16 to 20 minutes, beating occasionally with whisk, until sugar has dissolved and egg mixture reaches 160°F. Remove from heat; pour into bowl of electric stand mixer fitted with whisk attachment. Beat on high speed 2 to 3 minutes or until glossy peaks form and bowl has cooled to feel slightly warm. Still on high speed, slowly add 1 1/2 cups softened butter, one piece at a time, scraping side of bowl occasionally, until mixture is smooth, thick and shiny, 12 to 14 minutes. Beat in vanilla. If mixture separates, beat until smooth.