Pre heat the oven to 350F/ 180C / 160C fan. Grease a 9x9 inch baking tin.
Make the vegan buttermilk by mixing the soy milk and lemon juice and then leave to one side.
In a mixing bowl, add the sieved flour, cornstarch, baking powder, baking soda, salt and caster sugar. Mix well and create a well in the centre. Pour in the vegan buttermilk, sunflower oil and vanilla.
Gently fold the mixture until just combined, then pour out into the square baking tin and smooth over with a spatula.
Bake for 30 minutes. The cake is ready when it is golden, springy to the touch and pulling away from the sides of the tin. Leave to cool for 25 minutes in the tin and then turn out onto a wire rack to cool completely.
Meanwhile make the vegan mascarpone. Add the vegan cream cheese, coconut milk (creamy white part only), sugar and vanilla to a large mixing bowl. Use an electric whisk to beat the mixture until light and creamy, approximately 2 minutes. Cover and leave to cool in fridge.
Mix the espresso and dark rum in a jug. Cut the vanilla sponge into rectangles approximately 1.5 inches wide.
Use an 8x8 cake dish with tall sides. Dip only one side of each sponge ladyfinger into the espresso mixture and place into the dish. Spread over half of the vegan mascarpone. Dip the remaining ladyfingers in coffee and layer onto the mascarpone. Finish with the remaining mascarpone. Place the dish in the fridge to chill for a minimum of 4 hours or overnight.
Remove from the fridge and finish with thick dusting of cocoa powder. Slice and enjoy immediately.