Preheat the oven to 180°C/160°C fan/350°F/gas mark 4. Line a 20 cm/8 in square cake tin with baking parchment.
Place the roughly chopped carrots in a blender along with the oil, sugar, yogurt, vanilla extract and vinegar. Blend until completely smooth, with no lumps of carrot.
300 g (peeled weight) carrots, 145 g (160 ml/⅔ cup) neutral oil (I use olive, do not use coconut), 225 g (1 cup + 2 Tablespoons) caster or granulated sugar, 80 g (⅓ cup) Greek style soya yogurt, 2 teaspoons vanilla extract, 1 ½ teaspoons vinegar
Pour the blended mixture into a large bowl and use a balloon whisk to whisk in the cornflour, baking powder, bicarbonate of soda and salt, followed by the plain flour. Be careful not to over-beat the batter, stop mixing as soon as it is fully combined.
50 g (5 packed Tablespoons) cornflour (cornstarch), 2 ½ teaspoons baking powder, ¼ teaspoon bicarbonate of soda (baking soda), ¼ teaspoon salt, 270 g (2 ¼ cups) plain (all-purpose) flour
Pour the batter into the prepared tin and spread it level. Bake for 30-40 minutes until a skewer inserted into the centre comes out clean. Leave the cake to cool in the tin for 10 minutes then carefully turn it out onto a wire cooling rack and leave to cool completely.
Once the cake has cooled make the frosting. Place the cocoa powder, milk, sugar, butter, vanilla extract and a pinch of salt in a pan over a low heat. Whisk until melted and smooth then bring up to a simmer.
30 g (⅓ cup) cocoa powder, 80 g (6 Tablespoons) caster or granulated sugar, 180 g (¾ cup) unsweetened non-dairy milk (I use soy), 30 g (2 Tablespoons) vegan block butter, 1 teaspoon vanilla extract
Remove the pan from the heat and add the chocolate, stir until melted then set aside to cool and firm up to a spreadable consistency before using a palette knife to spread it over the cake. If you leave it too long and it sets too firm, simply place the pan over a low heat for a few seconds whilst stirring and it will become spreadable again.
125 g (4 ½ oz) dark chocolate