Grease a 21 cm x 21 cm / 8” x 8” square baking pan and line with non-stick baking paper. Preheat the oven to 180C (160C fan) / 350F.
Grate the carrots either using a box grater or mini chopper. Roughly chop the walnuts.
Whisk together the soya milk and vinegar in a large mixing bowl using a hand whisk or fork. Add the sugar, syrup and oil. Continue whisking until fully combined.
In a separate bowl, add the flours, baking powder, bicarbonate of soda, salt, mixed spice and cinnamon. Stir through to combine.
Fold the dry ingredients into the wet ingredients. Add the grated carrot and chopped walnuts and stir through until evenly distributed.
Transfer the mixture to the prepared tin. Using a spatula, distribute the mixture evenly in the tin and smooth the top. Place in the centre of the oven and bake for 45 minutes, or until a skewer inserted through the middle comes out clean and the top of the cake is springy to the touch.
Leave the cake in the tin for at least an hour, or until completely cool (it will continue to firm up as it cools), then peel off the baking paper and transfer to a chopping board. Using a bread knife, trim the four edges of the cake to neaten them up.
Meanwhile, place the cream cheese in a bowl. Sieve in the icing sugar, then beat using electric beaters until just combined (do not over-beat, otherwise the cheese may become runny). Taste test and add more sieved sugar, if desired. Beat once more to combine. Store the cream cheese in the fridge until needed.
Preheat a frying pan (skillet) on a medium-high heat. Add the walnuts and dry fry for 2 minutes, stirring continuously. Add the maple syrup and continue stirring for about 3 minutes, until the nuts are fully coated and the syrup has caramelised and become very sticky. Space out the nuts on a piece of non-stick baking paper. As they cool, the nuts will firm up and become shiny. Store in an airtight container in the fridge until ready to use.
Once the cake is completely cooled, distribute the cream cheese over the top of the cake using a knife. Slice the cake into squares, add the maple-glazed walnuts, then chill the cake in the fridge until ready to serve.
This cake will keep for up to five days in the fridge. It is also freezable (without the frosting). The cream cheese frosting is best added on the day that it is to be served as the lighter coloured cheeses (like Violife, Tofutti) can discolour over time.