In small saucepan, stir together 2 Tbsp of the water, 3 Tbsp of the sugar and the egg yolk. Cook over medium heat, stirring constantly, until mixture bubbles. Set aside. Allow to cool about 15 minutes.
In small mixing bowl, beat butter at high speed until smooth and creamy. Add 1 cup of the sugar, 2 Tbsp of the remaining water and the cooled yolk mixture. At medium speed, beat until smooth.
Beat in remaining sugar, adding some of the remaining 1 Tbsp water, 1 tsp at a time, until of spreading consistency. Beat in vanilla. Beat at high speed until smooth, adding remaining water, if necessary.
Servings: about 2 cups