Preheat the oven to 170 C. Grease an 8 inch round cake tin, or line it with non-stick baking paper. See notes for more on different cake tin sizes.
Melt the chocolate in the microwave in 10 second increments, stirring in between. Or you could use a double boiler method as well. Either way, don't over-heat the chocolate, if some lumps remain stir until they're melted through. Set aside.
In a mixing bowl, beat the butter and sugar with a hand mixer on low speed until pale and creamy. Add the yoghurt, milk, vanilla and beat slowly to combine. The yoghurt could cause a grainy appearance, don't worry.
Now pour in the melted chocolate and stir gently by hand to combine, using a silicone spatula preferably. Do not over-mix.
Sift in the flour, cocoa, cornflour, baking soda and salt. Stir briefly, then bit by bit, pour in the hot water, using the spatula to fold the batter as you go. The batter should be smooth, but be gentle while mixing.
Pour into the prepared tin, smoothen the top and bake for 30 to 35 minutes until a toothpick poked in the center comes out clean or with a few moist crumbs. Let the cake cool in the tin COMPLETELY and preferably overnight at room temperature. While there shouldn't be a majorly sunken center (over mixing the batter can lead to this) the center might fall very slightly as the cake cools, this is ok.
This cake is on the fragile side and will have some cracks on top as it bakes. Therefore use a sharp knife to slice it and if you're concerned, place it in the fridge for 30 minutes before cutting to guarantee neat slices.
Store at room temperature in an airtight tin for 3 to 4 days or in the fridge for about 10 days. Bring to room temperature before eating. It can also be frozen for longer. Happy baking!