Preheat the oven to 200C/180C Fan/Gas 6. Line your mini loaf tin (see notes for tips)
In a large bowl, or the bowl of a stand mixer, combine the butter, apple sauce and both sugars. Mix until combined.
Add the flour, baking powder, baking soda and spices and mix again. Add in the grated carrot, raisins and nuts - fold until all incorporated!
Scoop into the lined tin. Bake for 20-25 minutes, until golden brown and a skewer inserted comes out clean. Let cool fully on a wire rack before frosting.
For the frosting: combine the butter with half the icing sugar on a high speed. Add in the vanilla and gradually add in more icing sugar to reach a creamy/spreadable consistency! If it gets too stiff, add some vegan milk! Pipe/spread on the cakes and decorate with more nuts if using!