Preheat the oven to 350°F (175°C). Grease an 8.5- by 4.5-inch or 9- by 5-inch loaf pan and sprinkle with a thin layer of sugar.
In a bowl, whisk together the flour, cocoa powder, baking powder, espresso powder (if using), and salt.
In another bowl, whisk together the sugar, Greek yogurt, oil, eggs, and vanilla extract.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Pour the batter into the prepared loaf pan and bake for 50-60 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely. Slice and serve!
