Get ready a small pot and a heatproof mixing bowl that can fit snugly on the small pot. Fill the small pot with water until the surface of the water is 1-inch away from the bottom of the mixing bowl. Bring the water to a boil and turn down to a simmer.
Combine egg white and sugar in the heatproof mixing bowl. Place the heatproof bowl over the pot of simmering water and whisk with a wire whisk constantly until the mixture reaches 60C/140F. (If you don't have a thermometer, use a really fresh egg white - best is pasteurised - and whisk until you cannot feel any more sugar lumps.)
Remove the mixing bowl from the pot of simmering water and using an electric hand mixer (a stand mixer won't work as the quantity is too little), whisk the mixture on medium speed until it forms a stiff meringue. Continue beating on low speed until the meringue has cooled down - the mixing bowl should be barely warm to the touch.
Turn the mixer speed up to medium again and add in the diced butter tablespoonful by tablespoonful, beating until the butter has been incorporated before adding the next spoonful.
Once all the butter has been added in, keep beating until the mixture comes together into a nice-looking buttercream. Turn the speed down to low and beat in the vanilla, peppermint extract and cocoa powder. Taste and add more peppermint extract if desired. Frost as desired.
NOTES
- Make sure your butter is soft and diced before you start the recipe - you should be able to press into the butter easily with your finger but it shouldn't look glossy.