Using a rubber spatula stir together the egg whites, sugar and salt and in the bowl of an electric mixer over simmering water until egg-white mixture reaches a temperature of 160°F and the sugar is dissolved..
Place the bowl on the mixer and whip with the wire whip attachment on high speed until you have stiff peaks and the bowl is cool to the touch. This will take about 5-6 minutes. Meanwhile cut up butter into 1” pieces.
Switch to the paddle attachment.
With the mixer on medium-low speed begin adding the butter a piece at a time, adding another piece of butter when the previous one has been incorporated. Continue beating until the mixture begins to come together. This may take as long as 10-15 minutes.
If the buttercream does not come together, place the bowl and the whip attachment in the fridge for 10-15 minutes and beat again on low speed until smooth. Stop the mixer and scrape the bowl as needed.
Add the vanilla extract.