In a clean saucepan, combine the sugar and water. Boil without stirring until it reaches 240ºF (soft-ball stage) on a candy thermometer.

Meanwhile, in a stand mixer or using an electric mixer, beat the egg and egg yolk until light and ribbony.

As soon as the sugar is ready, turn the mixer to low speed and gradually pour the hot sugar syrup into the egg mixture. Increase the speed and whip until room temperature.

Add the butter, one piece at a time. Add the vanilla bean paste and whip until smooth and well blended.

Note: If buttercream is too soft: chill for 20 minutes in the mixing bowl, then return to the mixer and rewhip. If buttercream is too stiff: Place bowl over a pot of hot water for 20 seconds, then return to the mixer and rewhip.