Whisk together the flour, cocoa powder, baking soda, baking powder, and salt. Set aside.
Whisk together the eggs. Add the sugar, and whisk until combined. Add the mint extract, oil, and yogurt, and whisk until combined. Fold in the dry ingredients.
Whisk together the cream cheese and sugar until combined. Mix in the egg and mint extract, then fold in the flour. Add in enough green food colouring to reach desired colour.
Spoon the cheesecake mixture evenly over the cake batter (you don't have to use all of it), then pour the remaining cake batter on top.
Bake for 50 - 60 minutes or until a toothpick inserted into the centre comes out clean. Let cool in the pan for 10 minutes before inverting the cake onto a serving plate or cake stand. Allow to cool completely before glazing.
Add the chocolate to a heat-proof bowl, and set aside.
Add the heavy cream to a microwave-safe jug, and heat until hot. Pour the cream over the chocolate, and whisk until melted and smooth.
Leave to cool for 15 minutes before drizzling over the cake. For an even thicker ganache, allow to cool for longer.
*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.
Leftovers can be stored, covered, in the fridge for up to 2 - 3 days. You can bake this cake 1 day in advance. Allow to cool completely, then cover tightly and keep at room temperature or in the fridge until ready to glaze and serve.
This cake also freezes well for up to 2 months. Thaw overnight in the fridge before serving.
The calories are an estimate only.