Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.

Cream the butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the butter mixture, alternating with the milk, and mix until combined. Pour the batter into the prepared cake pan and smooth the top.

Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack.

Preheat the oven to 325°F (163°C). Beat the cream cheese and sugar until smooth. Add the eggs one at a time, mixing well. Stir in the vanilla extract and flour.

Pour the cheesecake mixture over the cooled cake layer in the same pan and spread it evenly.

Bake for 40-45 minutes or until the cheesecake is set but slightly jiggly. Let it cool for 10 minutes before transferring it to a wire rack to cool completely.

To make the custard, heat the milk and sugar in a saucepan over medium heat. In a separate bowl, whisk together the egg yolks and cornstarch. Gradually add the hot milk mixture to the yolks while whisking constantly.

Return the mixture to the saucepan and cook until thickened. Remove from heat and stir in the butter and vanilla extract. Let it cool.

To make the ganache, heat the cream in a saucepan until it begins to simmer. Pour the hot cream over the chopped chocolate and stir until smooth.

Once the cake and cheesecake layers are cool, spread the custard over the cheesecake layer and top with the chocolate ganache.