Start by preheating your oven to 175°C (350°F). Prepare your cake pan by greasing it well and lining it with parchment paper so the cake comes out easily later.
In a large mixing bowl, combine the melted butter and sugar until they blend smoothly. Add in the egg, mashed banana, yogurt (or sour cream), and vanilla essence. Stir everything together until the mixture looks creamy and well combined.
In a separate bowl, sift the flour, cocoa powder, baking soda, baking powder, and salt. Slowly add these dry ingredients into your wet mixture, stirring gently so you don’t overmix. Once combined, pour in the boiling water and stir until the batter becomes smooth and slightly thin.
Pour the batter into your prepared pan, spread it evenly with a spatula, and bake for about 35–40 minutes. Check with a toothpick—if it comes out clean, the cake is ready. Let it cool in the pan for 10 minutes, then move it onto a wire rack to cool completely.
For the espresso ganache, warm the heavy cream in a small saucepan over medium heat until it just begins to simmer. Place the chopped chocolate in a heatproof bowl, then pour the hot cream over it.
Let it sit for a minute so the chocolate melts. Stir in the espresso powder and butter until you have a smooth, glossy ganache. Allow it to cool slightly so it thickens but can still be spread.
Once your cake has cooled completely, spread the ganache over the top in an even layer. If you’d like, place the cake in the fridge for about 30 minutes to let the ganache set nicely before serving.