Special equipment: A candy thermometer
Place the egg whites and 1/3 cup of the sugar in the bowl of an electric mixer fitted with a whisk attachment. Beat on medium-high speed until the egg whites reach the soft peak stage.
Meanwhile, pour the remaining sugar and 1/3 cup water in a medium saucepan set over medium heat. Attach a candy thermometer to the side of the pan and bring to the soft-ball stage, without stirring, 240 degrees F.
The egg whites and syrup should be ready at about the same time. If one is ready before the other then you can remove the pan from the heat or stop whipping for a few minutes.
Continue to whip the egg whites on medium-high speed and slowly drizzle in the hot syrup, aiming the syrup between the side of the bowl and the beaters. Continue to whip until both the bottom of the bowl and the mixture are cool, 10 to 15 minutes. The mixture should be thick and will form firm peaks at this point. Beat in the salt. At this point you have an Italian meringue.
While still beating on medium-high, add the butter, a few pieces at a time. As the butter is added, the buttercream may appear to thin out some, but it will thicken into firm peaks once all of the butter is added. Beat in the vanilla extract. If the buttercream is still too loose, beat on high speed until thickened.
Use right away or refrigerate in an airtight container overnight. The buttercream may need to be beaten slightly to smooth out before using.
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