Preheat oven to 350°F. Grease and flour a 9-inch round cake pan.

In a mixing bowl, combine flour and baking powder. In a separate bowl, beat melted butter and sugar until light and fluffy. Add eggs one at a time, then vanilla. Gradually mix in dry ingredients. Pour batter into prepared pan.

Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Allow cake to cool completely.

Prepare custard by whisking together heavy cream, sugar, and vanilla in a saucepan over medium heat until thickened. Mix in vanilla pudding powder and cook for 2 minutes. Chill until set.

Cut the cooled cake horizontally into two layers. Spread custard over the bottom layer, then place the top layer on top.

For the ganache, heat heavy cream until just boiling, then pour over chocolate chips. Let sit for 2 minutes, then stir until smooth. Pour over assembled cake.

Chill the cake in the refrigerator for at least 2 hours before serving to set the ganache.