In the bowl of a stand mixer fitted with the whisk attachment, combine the sugar, egg yolks, and salt and beat on medium speed to mix. The mixture will be very thick and grainy.
Put 1 in [2.5 cm] of water in the bottom of a double boiler or a medium saucepan and bring to a gentle simmer over medium-low heat. Place the bowl with the yolk mixture over the simmering water and stir the mixture with a rubber spatula until the sugar is completely melted. Feel the mixture between your fingers to check for graininess. Once all the sugar has melted and the mixture is smooth, the syrup is hot enough to be safe to consume (see note).
Return the bowl to the stand mixer fitted with a clean whisk attachment and beat on medium-high speed until the egg foam is light, fluffy, and glossy and the bowl feel just about room temperature, 6 to 8 minutes (see note for visual cues below). If the egg foam isn't cooled sufficiently, the butter will melt when you add it.
Once the egg foam is whipped and cooled, turn the mixture speed to medium, add the butter 2 tablespoons at a time, and beat until incorporated. Turn the speed to low, add the vanilla, and mix until incorporated.
Use immediately or transfer to an airtight container and store int he refrigerator for up to 7 days or in the freezer for up to 1 month.
For the chocolate ganache: In a medium saucepan over low heat, warm the cream until just simmering. Turn off the heat and add the chocolate. Swirl the pan to make sure all of the chocolate is submerged in the hot cream. Let sit for 3 minutes and then gently stir until smooth.
Transfer the ganache to an airtight container and store at room temperature for up to 2 days, or in the refrigerator for up to 1 week.
Gently warm the ganache over a pan of simmering water, forming a double boiler, to a pourable consistency.
To assemble: Cut each cooled cake layer in half horizontally, to make a total of four layers. Put one layer on a turntable or serving plate and top with 3/4 cup of the buttercream. Use an offset spatula or knife to smooth it out. Repeat with two more layers and then top with the final layer, cut side down. Frost the cake with the remaining buttercream (there will be just enough buttercream to use in layers and coat the cake with a crumb coat). Chill the cake until firm, 2 hours.
Make the ganache. Separate about 1 cup [240 g] of the ganache and allow it to set to room temperature (you can place the separated ganache in the refrigerator and stir every few minutes until it is firm enough to spread on the cake, but being careful not to let it get too firm). It will now be spreadable and you can use it to create your ganache crumb coat.
Line a baking sheet with parchment paper. Place the crumb-coated cake onto a wire rack and set over the prepared baking sheet - you will be pouring quite a bit of ganache over the cake, so this setup will catch the excess.
Staring in the center of the cake, pour the ganache in a steady stream and work your way out to the edge in a spiral, making sure there are no bare spots. Continue pouring over the edges, until the sides are completely covered. The ganache should be smoothing itself out as our pour. If there are any ripples, ever so gently lift and set down whole baking sheet to settle the ganache; only do this right after you finish pouring or you may end up creating more ripples. Let the cake sit until set up enough that you can move it without disrupting the finish on the ganache, 15 to 20 minutes.
Run a metal spatula under the base of the cake to separate it from the wire rack before trying to lift it, or the ganache may tear.