Preheat your oven to 160 Fan / 180 C / 350 F / Gas 4 and line or grease and flour a 2lb loaf tin
In a bowl or jug whisk together the milk, yoghurt, oil and vinegar
In a large bowl mix together the flour, baking powder, baking soda, sugar and spices
Grate the carrot (peeling them first is up to you!)
Add the milk mixture the the bowl of dry ingredients and stir everything together well, making sure there are no sneaky flour 'pockets' at the bottom of the bowl
Once everything is well mixed stir in the grated carrot then pour into your prepared tin
Bake for 1 hour 15 minutes until the cake is well risen and springy. You can test by inserting a skewer into the centre of the cake - if it comes out clean with no raw cake clinging to it the cake is done. Otherwise return the cake to the oven for a few minutes and repeat the testing process
Allow to cool in the tin for a few minutes before carefully lifting out onto a wire rack to cool completely
While the cake is cooling toast the walnuts in a dry frying pan. I do this over a very high heat (for speed) but watch them like a hawk, tossing the pan frequently. Set aside to cool then roughly chop or crumble in your hands
Once the cake is completely cool beat together the vegan butter, icing sugar and grated lemon zest until very pale and fluffy. If you're doing this by hand rather than in a stand mixer with the paddle attachment you'll need to soften the butter first. Once it's well beaten, stir in the vegan cream cheese until well mixed
Spread the buttercream frosting all over the top of the cooled cake then sprinkle over the walnuts
Notes
Store the cake in an airtight container at room temperature for 2-3 days. You can also store in the fridge for a little longer but it's best served at room temperature
This loaf cake also freezes really well. I slice it then wrap a couple of slices in foil before freezing
Recipe by The Cook & Him at https://thecookandhim.com/recipes/vegan-carrot-loaf-cake-with-lemon-cream-cheese-frosting/