Preheat the oven to 150'C (fan)/170'C (conventional) - 300'F (fan)/340'F (conventional) and grease and flour 2 x 8 inch round cake tins.
Start by whisking together the butter, oil, and both types of sugar. Not aiming to aerate the mixture here, just to get everything smooth and well combined.
Next, add in the eggs and whisk well once again. It should look smooth and emulsified. Then, add in the yoghurt, milk powder, and spices and mix well once again.
Whisk in the flour, baking powder, baking soda, and salt until no dry flour remains (small lumps are fine).
Add in the grated carrots and chopped walnuts and fold until well incorporated.
Split the batter equally between the tins and bake for 40-45 minutes or until golden brown and a skewer comes out clean.
Take half of the butter (100g) and place this into a saucepan over a low heat. Once the butter has melted, switch to a medium/medium-low heat and stir every 30 seconds or so. It will start to sputter and spit before turning translucent. At this stage the milk solids will start to separate and gradually caramelise. Once they turn a deep golden brown, transfer the brown butter into a separate bowl and allow to cool completely to room temp.
Place the remaining 100g butter into a stand mixer with a paddle attachment/bowl and whisk (preferably electric). Cream the softened butter on a medium low speed for around 5 minutes or until slightly pale. Then, add in the cooled brown butter, icing sugar, vanilla, and salt. Continue to mix on a low speed until incorporated.
Once incorporated, mix on medium speed for a further 5-7 minutes. Stop every minute or so to scrape the
of the mixer and give everything a once over.
Place the just-out-of-the-fridge cream cheese into a separate bowl and lightly beat with a spatula to soften (20 seconds is all it requires). Add the cream cheese to the buttercream and mix on the slowest speed until incorporated. Avoid over-mixing here as that can cause the cream cheese to start to split - this will then lead to the frosting loosening up.
Spread the frosting over the first layer of cake, then place the second layer on top and repeat.
Cover the sides of the cake with frosting and smooth it out to the best of your ability. Feel free to design a little swirl on top if desired.
I like to cover the lower portion of the sides with crushed walnuts and some glacé mixed peel on top.
Optional: Refrigerate the decorated cake for around 30 minutes for the frosting to firm up. This will help with ensuring clean slices.
