With an electric hand mixer on medium speed, mix the egg whites, sugar, and vanilla extract in a glass or steel bowl over simmering water until the egg white mixture reaches 150 degrees F.
Take the bowl off the heat. With an electric mixer on medium-high speed, whip the egg whites until they become fluffy and double in volume. Allow the egg mixture to cool to room temperature, about 15 minutes.
Using an electric mixer again, whisk the egg mixture over medium speed and slowly add the cubes of butter, a few at a time. Whip until the buttercream is stiff and very thick. If the mixture is too runny and/or won't thicken up after 8 minutes, place the bowl in the refrigerator for about 15 minutes, then re-whip until it comes together (do not over chill in the refrigerator as the frosting will solidify and become difficult to spread).
Pipe frosting over the cooled cupcakes.