In a clean metal bowl of a stand mixer or other heatproof bowl, add egg whites and granulated sugar.
Balance the bowl over a pot with 1 inch of gently simmering water, ensure that the bottom of the bowl isn’t touching the water. Whisk continuously as the egg whites warm-up and keep whisking until all the sugar has dissolved or the temperature reads 160°F (71°C) on an instant-thermometer. Don’t stop stirring or some egg whites may overcook on the edges of the bowl.
Place the bowl of cooked egg whites in your stand mixer, or add them to your stand mixer bowl, fitted with the whisk attachment and beat on medium-high speed until a meringue with stiff peaks forms and the meringue has cooled down to room temperature. When you touch the sides of the bowl they shouldn't feel warm.
While the egg whites are beating, melt the chocolate. Place the chocolate in a microwave-proof bowl and melt it in the microwave for 20-30 seconds at a time, stirring after each time. Once about 2/3 of the chocolate has melted, remove it from the microwave and stir it to further melt it and combine it. Let the chocolate cool to room temperature (but don't let it get too cold or harden again.)
With the mixer on medium-high speed, feed in a cube of room temperature butter at a time, allowing it to incorporate fully before adding the next cube.
At this point, the meringue can suddenly appear split or curdled. Just keep beating the mixture until it comes together into a thick and fluffy buttercream. This can take a lot of beating so don't give up if it doesn't seem to come together - it will. You want to keep mixing it until it loses the greasy look and it's just thick and fluffy. See the notes for troubleshooting.
Once the mixture is thick and fluffy, beat in the melted chocolate, salt, and vanilla until thick and fluffy.
Switch to the paddle attachment and beat on low speed for 10 minutes to remove some of the larger air bubbles in the buttercream.