In large bowl, whip egg yolks and white on medium-high speed with electric mixer until very thick and pale, about 6 minutes.
Meanwhile, in small heavy saucepan, combine sugar, water, corn syrup, and salt; stir gently to combine. Cook over medium heat without stirring until candy thermometer registers 236°-240°F "soft ball" stage. Immediately remove pan from heat.
With mixer on medium speed, slowly add sugar syrup to the eggs down the side of the mixing bowl (Do not let the syrup fall directly into the egg whip). Continue whipping on high speed until mixing bowl has cooled enough to touch, about 5 seconds. Reduce mixer speed to medium-low; add butter, one chunk at a time, beating until butter is fully incorporated after each addition. Mixture will begin to look curdled, like it is separating, but will come back together as you keep beating in butter. Add vanilla and melted, cooled chocolate into the buttercream. Mix until incorporated, scraping down sides of the bowl. 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 icing