If this is your first time making SMBC, I would recommend watching the demonstration video below to understand how things should look at certain stages so you know you're on the right track :)
Begin by separating your egg whites from your egg yolks (if using fresh eggs). Do this carefully as there must not be any yolks in the whites, otherwise this will prevent the whites from whipping up properly when we make our meringue.
In a heat proof bowl, whisk together the egg whites and caster sugar, and gently heat the mixture over a double boiler. Keep gently mixing the mixture so it heats evenly. The goal is to get a smooth texture without over-cooking the egg whites. After a few minutes, check the mixture by rubbing it in between your fingers. If you can't feel any sugar granules then it is done. If you're not using pasteurised egg whites, then ensure the mixture has reached 75 °C so that it is safe to eat.
Transfer the mixture into a stand mixer (see note 1), and using the whisk attachment, whisk the egg whites and sugar on medium-high speed (speed 8 on KitchenAid) for 10-15 minutes until the mixture is cool and stiff peaks have formed. The final product is what we call a meringue.
While your meringue is whipping up, melt your dark chocolate over a double boiler or in the microwave (see note 2). Set aside to cool.
Turn down your mixer to a medium speed (speed 6 on KitchenAid) and slowly add in the unsalted butter, about a tablespoon at a time (see note 6). It is important to ensure that the butter is at room temperature (soft enough to make an indent with your finger, but not melted or losing it's shape). See note 3
Once all the butter is mixed in, add in your vanilla and continue to mix your buttercream until it is smooth in consistency. At some stage it may look like the buttercream is curdling, but this is totally normal! Just let your mixer do it's thing and it will come together :)
Lastly, slowly pour your chocolate into your buttercream while your mixer is on a medium speed until the chocolate is well incorporated. Your buttercream is now ready to use, but if you find it's a little soft after adding in the chocolate, let it chill in the fridge for 30 minutes and then rewhip it and it'll be good to go!