In the bowl of an electric mixer, add the egg whites and sugar. Whisk briefly by hand until combined.
Fill a saucepan with a few inches of water and bring to a simmer over medium heat. Place the mixer bowl on top of the saucepan to create a double-boiler. Stirring intermittently, heat the egg mixture until it reaches 150 to 160 on a candy thermometer.
Once hot, carefully return the mixer bowl to the stand mixer. Fitted with the whisk attachment, whip the egg white mixture on high until stiff peaks, about 8 minutes. When done, the outside of the mixer bowl should return to room temperature.
Stop the mixer and swap the paddle for the whisk. With the mixer on low, add in the vanilla and butter, a couple tablespoons at a time. Once all of the butter has been added, turn the mixer up to medium-high and mix until smooth. If the mixture looks curdled, just keep mixing until it is smooth (this could take up to about 5 minutes). If it appears soupy, place the mixer bowl in the fridge for 10 to 15 minutes, then mix until smooth. Tint with gel food coloring, if desired.
Recipe may be doubled to frost and decorate a larger cake.