German Buttercream

Combine egg in a compact, dense saucepan and whisk vigorously using a fork until the mixture is smooth. Introduce sugar and milk into the saucepan, blending them thoroughly. Place the saucepan over a moderate heat setting on your stovetop and gently stir the mixture with a fork constantly, allowing it to reach a gentle simmer. Continue stirring rapidly until the mixture thickens into a thin, creamy consistency. Set the saucepan aside and allow it to cool completely, approximately 1 hour.

Combine butter in a bowl using an electric mixer until the mixture is light and airy, taking around 5 minutes. Gradually add the cooled custard to the bowl, introducing small amounts at a time and blending well after each addition. Incorporate rum and vanilla extract into the mixture, stirring continuously until the buttercream becomes very light and fluffy.