Preheat the oven to 350 degrees F. Grease and line 3 8-inch cake pans with parchment paper rounds.
To make the cake: Separate the egg yolks from the whites and place them into two separate bowls.
Add the egg whites to the bowl of a stand mixer fitted with the whisk attachment and beat on medium speed for 2-3 minutes until they form soft peaks.
Slowly add 1/3 cup of the sugar and continue beating until the whites hold stiff peaks. Transfer the egg whites to a bowl and set aside.
Clean the bowl of your stand mixer and add the egg yolks and the remaining sugar.
Beat the eggs until light in color.
Add the vanilla and sift in the cocoa powder. Mix on low speed until combined.
Fold one-third of the egg whites into the chocolate mixture, making sure not to deflate the batter. Repeat the process with 2 more additions of egg whites to the batter until it is light and fluffy.
Evenly divide the batter amongst the prepared cake pans and bake for 10 to 12 minutes.
Remove the cake pans from the oven and let them cool on a wire rack for 5 minutes before transferring them to the refrigerator while you make the mousse.
To make the mousse: Place the chopped milk chocolate and the semi-sweet chocolate into 2 separate medium-sized bowls.
Bring 2/3 cup of heavy cream to a simmer in a small saucepan over medium heat. Add 4 Tablespoons of the hot cream to the milk chocolate and pour the remaining hot cream over the semi-sweet chocolate. Let the mixture sit for 1-2 minutes to soften the chocolate, then stir, so the chocolate has a smooth consistency. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment, beat the remaining 1 cup of heavy cream to form soft peaks.
Fold 1 cup of the whipped cream into the milk chocolate mixture and the remaining 1 cup into the dark chocolate mixture. Return the bowls to the refrigerator until needed.
Remove the cake layers from the tins and place one layer on a round wire rack. Dollop the semi-sweet chocolate mousse on top of the cake layer and smooth it out with an offset spatula.
Place the second cake layer over the semi-sweet chocolate mousse and repeat the process with the milk chocolate mousse. Top with the final cake layer and place the cake in the refrigerator while you make the ganache.
Place the semi-sweet chocolate pieces into a small glass bowl. Heat the heavy cream in a small saucepan over medium heat until it reaches a simmer.
Pour the hot cream over the chocolate, Let the mixture sit for 1-2 minutes to soften the chocolate, then stir, so the ganache has a smooth consistency. Transfer the ganache to a bowl with a pour spout.
Remove the cake from the refrigerator, place the wire rack over a large baking sheet to catch any chocolate drips, and slowly pour the ganache over the top and sides of the cake. Smooth out any divots or bumps using an offset spatula. You can scrape and re-heat any extra dripped chocolate from the baking sheet to reuse.
Slice and serve.