Preheat the oven to 160 °C (fan). Line two 20cm/7.8 inch spring-form cake tins with greaseproof paper. Set aside.
Place the walnut pieces, caster sugar and light brown sugar in a food processor and process until sandy textured with no chunks of walnut remaining.
60 g walnut halves, 180 g caster sugar, 45 g light brown sugar
To the food processor, add the vegetable oil, vegan yoghurt, soy milk and instant espresso powder then run again until the mixture is thick and smooth. Set aside.
200 g vegetable oil, 200 g vegan yoghurt, 4 teaspoon instant espresso powder, 4 tablespoon soy milk
In a medium bowl, sieve together the plain white flour, corn starch, baking powder and bicarbonate of soda. Add the wet ingredients to the sieved dry ingredients and mix until just combined - the mixture will be a thick batter.
220 g plain white flour, 2 tablespoon corn starch, 2 ½ teaspoon baking powder, ½ teaspoon bicarbonate of soda
Divide the batter between the two prepared cake tins and smooth the tops of the batter with the back of a spoon. Bake the two cakes for 25 minutes.
Remove the cakes from the oven and turn the oven temperature to 140 °C. Leave the cakes to cool in their tins for 15 minutes. Remove the tins and transfer the cakes to a wire cooling rack to cool completely before transferring to the fridge to chill. While the cakes cool, make the candied walnuts, coffee buttercream and coffee syrup.