These quantities will make enough icing for a 9 inch cake, plus some extra.
In a large metal bowl over a saucepan of simmering water whisk the egg whites and sugar occasionally until the sugar has completely melted. You will know it is completely melted when you can feel any sugar granules when you rub a bit between your fingers.
Take the mixture off the heat, wipe the bottom of the bowl to prevent any water condensation getting into the mixture as this will prevent it from whipping. Whisk with an electric mixer until the mixture is white and glassy and doubles in size. Whisk in the vanilla.
Add the butter, a third at a time and continue to whisk until the mixture thickens and comes together. This can take quite a few minutes – don’t panic, just carry on whisking.