Preheat the oven to 180C/350F/Gas 4. Grease a 10-inch bundt pan, and set aside.
Whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Set aside.
Whisk together the eggs. Add the sugars, and whisk until combined. Add the melted butter, yoghurt, and pumpkin and whisk until combined. Fold in the dry ingredients.
Pour half of the batter into the prepared pan.
For the 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 Frosting
Whisk together the icing sugar, cream cheese, heavy cream, and vanilla extract until smooth, fairly thick and pourable. Add more heavy cream if needed.
Pour over the cooled cake (or pipe it on using a piping bag), then slice and serve.
Notes
*Make your own cake flour! Weigh out 3 cups (375g) of plain/all-purpose flour, remove 6 tablespoons, and replace with 6 tablespoons of cornflour/cornstarch. Sift well.Leftovers can be stored 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 in the fridge until ready to glaze and serve.This cake also freezes well for up to 3 months. Thaw overnight in the fridge before serving.