Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. In a mixing bowl, whisk together the flour, baking powder, and salt. In another bowl, blend the eggs, milk, vanilla extract, and sugar until well combined. Slowly pour the wet mixture into the dry ingredients, stirring until smooth. Divide the batter between the prepared pans and bake for 25–30 minutes. Allow the cakes to cool completely.

While the cakes cool, heat 2 cups of milk over medium heat until steaming. In a separate bowl, whisk egg yolks with sugar until pale. Gradually temper by adding hot milk while whisking. Return to saucepan and cook until thickened, about 10 minutes. Stir in vanilla extract. Transfer to a bowl and cover with plastic wrap.

To create the ganache, heat 1 cup of cream in a saucepan until it simmers. Remove from heat, add chopped dark chocolate, and let sit for 5 minutes. Whisk until smooth and glossy.

To assemble, place one cooled cake layer on a serving plate. Spoon custard onto the center, spreading it evenly. Place the second cake layer on top and pour the warm ganache over the top, allowing it to drip down. Chill for at least 30 minutes before slicing.