Preheat the oven to 160°C (320°F). Grease a 9-inch springform or round cake tin.
Dissolve the instant coffee powder in the boiling hot water. Set aside to cool completely.
Sift the cocoa powder, flour, baking powder, baking soda, and salt into a large bowl. Set aside.
In a separate bowl, beat the butter, brown sugar, and caster sugar together until pale and creamy.
Add the eggs and vanilla extract, and beat until well combined.
Add a few tablespoons of the flour mixture into the butter mixture to stabilize it, then beat in the yoghurt until smooth.
Alternately add the remaining flour mixture and the cooled coffee, starting and ending with the flour mixture. Fold gently until smooth.
Pour the batter into the prepared tin. Bake for 1 hour to 1 hour 10 minutes, until a toothpick inserted into the center comes out clean.
Cool completely in the tin at room temperature.
For the ganache, heat the cream and instant coffee powder together until warm and just barely simmering.
Pour the hot cream mixture over the chopped chocolate and let it rest for 1 minute, then stir until smooth and glossy.
Chill the ganache for about 20 minutes, until it thickens to a spreadable, pourable consistency.
Pour the ganache over the cooled cake, smoothing it around the top and sides with an offset spatula.
Let the ganache set at room temperature before slicing.