In large bowl, beat egg whites with electric mixer to soft peaks.
In small heavy saucepan, combine sugar, water, corn syrup and salt. Stir gently to combine. Cook mixture over medium heat with no stirring until thermometer registers 236°-240°F (soft ball stage). Immediately remove pan from heat.
Begin whipping egg whites again at high speed. Slowly and carefully down the side of the bowl, add hot sugar syrup to the whites. Don’t allow the syrup to fall directly into the whip. Continue whipping at high speed until bowl has cooled enough to touch for 5 seconds. Reduce mixer speed to medium-low; add butter, one piece at a time, until incorporated. Mixture will begin to look curdled, like it is breaking or separating, but will come back together as you continue adding butter. Add vanilla. Continue whipping until desired consistency.
Use immediately or cover and refrigerate up to 1 month. Let buttercream come to room temperature and beat until smooth before using.
Makes about 6 cups.