Preheat the oven to 150°C (300°F) (without fan).
Grease and line 2 x 26 cm (10 inch) round cake tins. (I made 3 x 20 cm (8 inch) cakes plus 2 muffins and gave the extra cake to my neighbours, but you could also make a 3 tiered cake, if you wish.)
Dissolve the instant coffee in the hot water in a small saucepan over high heat.
Add the chocolate and stir until the chocolate has melted.
Take the saucepan off the heat and leave it to cool slightly.
Sift the sugar, flour, cocoa powder, baking soda and baking powder into a large bowl.
In the bowl of a food mixer, beat the eggs with the whisk attachment until they are thick and pale yellow in colour.
Slowly whisk in the oil, natural yoghurt, vanilla extract and chocolate mixture.
Add the wet ingredients to the bowl of dry ingredients and beat until everything is well incorporated. I have two bowls for my KitchenAid and used the smaller bowl for the wet ingredients, and the larger bowl for the dry ingredients, mixing everything together at the end with the flat paddle attachment.
Divide the mixture between the cake tins.
Bake for about 50-65 minutes if using 26 cm (10 inch) cake tins, or about 40-45 minutes for 20 cm (8 inch) cake tins.
The cakes should be ready when the sides of the cake start to come away from the tin and a skewer inserted in the middle of the cake comes out clean.
Invert the cakes onto a cooling rack and leave for about 5 minutes before removing the tins, and let the cakes completely cool down.