Make the cupcakes
Preheat the oven to 350°F. Line a muffin pan with paper liners and set aside.
Put the cocoa powder in a bowl and pour the boiling water over it, whisking until you have a smooth paste. Add the sour cream and salt and whisk to combine. Set aside to cool to room temperature.
In a large bowl, sift together the cake flour, baking powder, and baking soda. Set aside.
Place the egg yolks in the bowl of an electric mixer with the whisk attachment. Add the brown sugar and begin mixing on medium-high speed. Drizzle in the oil in a slow, steady stream to emulsify the mixture as if you were making a mayonnaise. Remove the bowl from the mixer and set aside. (Note: Unless you don’t mind whipping egg whites by hand, you will need to transfer the yolk-oil mixture to another bowl and wash the mixer bowl and the whisk attachment. Or, if you have an extra bowl for your electric mixer, you will have to wash only the whisk.)
Place the egg whites in the clean bowl of the electric mixer with the clean whisk attachment and, while whipping on medium-high speed, gradually add the granulated sugar, continuing to whip until soft peaks form. Set aside.
Add the cocoa mixture to the yolk-oil mixture and use a whisk (by hand) to combine. Pour this mixture into the bowl of dry ingredients and whisk by hand for 1 minute to aerate.
Fold in the whipped egg whites in 3 additions using a rubber spatula and taking care not to deflate the whites.
Fold in the chopped chocolate and vanilla extract.
As soon as you’ve finished the batter, fill the muffin pan and bake your cupcakes. Scoop the batter into the prepared muffin pan, using about 1⁄3 cup batter per cupcake and dividing the batter evenly among the wells of the pan.
Bake for 22 to 24 minutes, until the tops are nicely domed with a few cracks on top and a skewer inserted in a cupcake comes out with a few moist crumbs clinging to it. Don’t open the oven for at least the first 20 minutes to get the best rise from the cupcakes. After 20 minutes, you can check the cupcakes and bake for a few minutes longer as needed.
Remove the muffin pan from the oven and cool on a wire rack for 5 to 10 minutes, before removing the cupcakes from the pan. Continue to cool the cupcakes to room temperature before icing them.
Make the buttercream and frost the cupcakes
Use the tip of a paring knife to scrape the seeds from the vanilla bean. Reserve the scrapings to add to the buttercream later and save the pod to make vanilla bean sugar.
Place the egg whites and sugar in a bowl (it’s easiest just to use the bowl of the electric mixer) placed over a pot of simmering water (the bottom of the bowl the water should not touch) and stir with a rubber spatula until the mixture begins to smell like cooked eggs, 8 to 10 minutes. The mixture should not be so hot that you can’t put your finger in it, but it should be too hot to hold your finger in it for long. If you want to check the temperature with a thermometer, it should read 160°F.
Remove the bowl from the heat, place it in the electric mixer with the whisk attachment, and whip on medium-high speed until the egg white mixture is very thick and has cooled to room temperature (it should look as thick as shaving cream), 10 to 15 minutes. The egg white mixture will cool as it whips. Feel it with your finger at this point—it should feel like it is no longer warm enough to melt butter.
Turn the mixer to medium speed and add the butter gradually, about a tablespoon at a time, until all the butter is fully incorporated. When you get halfway through adding the butter, scrape down the bowl. Turn the mixer up to high speed and whip the buttercream for 1 minute.
Add the vanilla bean seeds, vanilla extract, and salt and whip for 30 seconds more. Scrape down the bowl again and be sure all the flavorings are well mixed in.
To create spikes of buttercream (as pictured), transfer the frosting to a pastry bag fitted with a 1/4 or 5/16-inch plain tip. Pipe dollops of buttercream onto the cupcake, working your way from the outside rim to the middle of the cupcake.