In a mixing bowl, whisk together flour, baking powder, and salt until combined. In another bowl, beat sugar and eggs until pale and fluffy. Gradually mix in milk and vanilla extract until smooth, then fold in dry ingredients to form a batter.

Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. Divide batter into pans and smooth tops. Bake for 25-30 minutes or until golden and a toothpick comes out clean. Cool in pans for 10 minutes then transfer to wire rack to cool completely.

In a saucepan, heat milk over medium heat until steaming. In a bowl, whisk egg yolks and sugar until pale. Gradually whisk hot milk into egg mixture to temper eggs. Pour back into saucepan and cook, stirring constantly, until thickened (about 5 minutes). Remove from heat and stir in vanilla extract.

In a small saucepan, heat heavy cream over medium-high heat until bubbling around the edges. Remove from heat, add chopped chocolate, and let sit for 5 minutes. Stir until smooth.

On a serving plate, place one cake layer. Spread half of the custard on top, then gently add the second cake layer. Pour the ganache over the top, allowing it to drip down the sides. Chill in the refrigerator for at least 2 hours before serving.