Preheat the oven to 160℃/140℃ fan/325℉/gas mark 3. Grease and line two 20 cm/8 in round, 5 cm/2 in deep cake tins.
Place the cocoa powder in a large bowl and whisk in the boiling water with a balloon whisk. Add the chopped chocolate and espresso powder and whisk until melted and smooth.
60 g (¾ cup) Dutch processed or black cocoa powder, 380 g (1 ½ cups + 4 teaspoons) boiling water, 150 g 60-75% dark chocolate, 2 teaspoons instant espresso powder or 1 Tablespoon instant coffee granules
Whisk in the oil, sugar, yogurt and vanilla extract.
147 g (⅔ cup) oil (olive, sunflower, vegetable or canola), 300 g (1 ½ cups) light brown soft sugar, 180 g (¾ cup) plain vegan yogurt, 2 teaspoons vanilla extract
Whisk in the baking powder, bicarbonate of soda and salt, followed by the plain flour. Mix until no dry lumps remain but be careful not to overbeat the batter.
2 teaspoons baking powder, 1 ¼ teaspoons bicarbonate of soda, ½ teaspoon salt, 340 g (2 ¾ cups) plain (all-purpose) flour
Divide the batter between the prepared tins (use a scale for accuracy) and bake for 45-50 minutes until a skewer inserted into the centre comes out clean.
Allow the cakes to cool in the tins for 20 minutes then carefully turn them out onto a wire rack and leave to cool completely. Once cool store in an airtight container.