Begin by separating your egg yolks from your egg whites. Once separated, add your egg yolks to the bowl of a stand mixer, and using the whisk attachment, mix on a medium high speed for 5 minutes until the yolks are a pale yellow colour.
While your egg yolks are mixing, begin working on your sugar mixture. Add your sugar and water to a saucepan, and mix until the sugar granules are coated in the water. Place your saucepan on a low-medium heat, and without mixing, let the sugar heat to a temperature of 115 °C.
Once the sugar reaches 115 °C, take it off the heat immediately and with your mixer on a low-medium speed, begin slowly pouring the bubbling mixture into your egg yolks (see note 1).
Once all the sugar is added in, turn your mixer up to medium-high speed and mix for 5-8 minutes, or until your bowl is cool to the touch (see note 2).
Once the egg yolk/sugar mixture is at room temperature, begin to add in your unsalted butter a tablespoon at a time, letting each tablespoon mix in well before adding the next.
Once all the butter is mixed in, add in your vanilla and salt, and then continue to mix for a few minutes until your buttercream is smooth.
Lastly, chop up your chocolate into small pieces and then place in a microwave safe bowl. Melt in the microwave for 20 second bursts at a time, mixing in between each burst until fully melted. Allow to cool for 10 minutes.
Turn your mixer onto a low-medium speed, and slowly stream in the melted chocolate. Once all the chocolate has been added in, turn your mixer up to a medium high speed and mix until the chocolate is fully mixed in. Once complete, if you frosting feels a little too soft, then pop it into the fridge for 30 minutes, and then rewhip it until smooth.