First, preheat your oven to 175°C (350°F), or 160°C (320°F) for a fan oven. Grease a 28 × 15 × 8 cm loaf mould thoroughly and line it with baking paper, leaving some overhang to make the finished loaf easier to remove.
Next, combine the hot water and espresso powder in a small bowl. Stir until the espresso powder has completely dissolved, then set the mixture aside to cool. Make sure it is not hot when added to the batter.
Meanwhile, add the all purpose flour, baking powder, baking soda and salt to a bowl. Whisk everything together until evenly combined. This helps distribute the raising agents throughout the flour and gives the loaf an even rise.
In a separate large bowl, whisk the melted butter with the granulated sugar and dark brown sugar. Continue mixing until the sugars are well incorporated and the mixture looks smooth.
Then, add the eggs one at a time and whisk until combined. Avoid overmixing at this stage. You only need to mix until the eggs are incorporated and the batter looks smooth.
Pour in the cooled espresso mixture, followed by the buttermilk, Greek yogurt and vanilla extract. Whisk gently until the wet ingredients are fully combined. The espresso gives the cake its main coffee flavour, while the buttermilk and yogurt help create a tender crumb.
Gradually add the dry ingredients to the wet mixture. Using a spatula, gently fold everything together until no large patches of flour remain. Do not overmix the batter, because excessive mixing can make the espresso loaf dense instead of soft.
Pour the batter into the prepared loaf mould, making sure it fills no more than approximately two thirds to three quarters of the mould. Smooth the surface gently with a spatula if needed.
Place the loaf in the preheated oven and bake for approximately 40 to 50 minutes. Start checking around the 40 minute mark, as baking times can vary between ovens. Insert a skewer into the center of the loaf. It should come out with a few moist crumbs attached, but there should be no wet batter.
Once baked, remove the loaf from the oven and allow it to cool in the mould for 10 to 15 minutes. Then, carefully lift it out using the parchment paper and transfer it to a wire rack.
While the loaf is cooling slightly, dissolve the espresso powder in hot water. Stir until completely smooth.Next, add the heavy cream and icing sugar to a small saucepan. Heat gently over low heat, whisking until the icing sugar has dissolved. Add the dissolved espresso and continue heating for 2 to 4 minutes, whisking occasionally. Do not allow the cream mixture to boil. Remove the espresso cream glaze from the heat and let it sit for 2 to 3 minutes. Then, pour the warm glaze slowly over the still warm espresso loaf, allowing it to spread across the top and gently soak into the cake.
Finally, allow the glazed loaf to sit for 5 to 10 minutes before slicing. This gives the warm coffee glaze a little time to settle into the cake while the loaf remains soft and fragrant. Slice and serve while slightly warm or allow it to cool completely.