Preheat the oven to 180C/350F/Gas 4. Grease a 10-inch bundt pan, and set aside.
Whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
Whisk together the eggs. Add the sugars, and whisk until combined. Add the vanilla, melted butter, and yoghurt, and whisk until combined. Fold in the dry ingredients.
Pour half of the batter into the prepared pan.
For the Cheesecake Filling
Using a handheld or stand mixer fitted with the paddle attachment, beat the cream cheese and sugar until combined. Beat in the egg and vanilla, then fold in the flour.
Spread the cheesecake mixture evenly over the cake batter, then pour the remaining cake batter on top.
Bake for about 60 minutes or until a toothpick inserted into the centre comes out clean with moist crumbs.
Let cool in the pan for 10 minutes before inverting the cake onto a wire rack or serving plate to cool completely.
For the Ganache
Microwave the heavy cream until very hot, but not boiling.
Place the chocolate chips in a heat-proof bowl. Pour the heavy cream over the chocolate chips and whisk until completely melted and smooth. Whisk in the vanilla.
Leave to cool for 5 - 10 minutes, then drizzle over the cooled cake, and serve.
For a thicker ganache like pictured, leave to cool completely, then pour it onto the cake, and spread out as desired.
Notes
*Make your own cake flour! Weigh out 2 and 1/2 cups (312g) plain/all-purpose flour, remove 5 tablespoons, and replace with 5 tablespoons of cornflour/cornstarch. Sift well.You can bake this cake 1 day in advance. Allow to cool completely, then cover tightly and keep in the fridge until ready to frost and serve. This cake also freezes well for up to 2 months. Thaw overnight in the fridge before frosting and serving.