Place the sugar and water in a medium saucepan and swirl the pan until the sugar is fully immersed in water. Place the saucepan over medium heat until the sugar dissolves and comes to a gentle simmer. Lower the heat to low and place the lid on the pan and allow the mixture to simmer for a couple minutes.

Meanwhile, place the egg yolks in the bowl of a stand mixer, fitted with the whisk attachment, and turn the mixer up to high speed. Let it whip while the sugar is done cooking.

Use a candy thermometer to see when the sugar reaches 240F (116C), then lower the mixer to medium speed and slowly drizzle the hot sugar syrup into the thick and foamy egg yolks, while they are whipping. Turn the mixer back up to high speed and let it whip for 5-10 minutes, until the yolk mixture is very pale and fluffy and is cool to the touch or no longer warm.

Turn the mixer back down to medium speed and add in the butter, 2 Tbsp of butter at a time, mixing until each chunk is fully combined and the buttercream looks smooth and creamy. Scrape the sides and bottom of the bowl, add in the vanilla and salt and turn the mixer up to high speed for 1-2 minutes.