Preheat the oven to 175˚C/155˚C fan/350˚F/gas mark 4. Grease and line two 20.5cm (8”) round cake tins with baking paper.
Mix together all of the dry ingredients. Peel the carrots and grate them into a large bowl. Add the milk, apple cider vinegar, eggs and vegetable oil and mix them together. Sift the dry ingredients into the bowl and mix until fully combined.
Pour the mixture evenly into the two prepared tins and smooth over the top to level out the batter.
Place in the preheated oven and bake for 45 minutes, or until a skewer inserted into the centre of the cake comes out clean.
Allow the cakes to cool in the tins for 15 minutes, then remove from the tins and wrap in cling film until ready to use. Store the wrapped cakes in the refrigerator for up to one week.
Mix together the butter, icing sugar, vanilla extract and milk for the buttercream in an electric stand mixer until light and fluffy. In another bowl, mix the cream cheese and the icing sugar for the filling. Add one fifth of the buttercream to the cream cheese mixture, mixing well until fully combined.
Make sure the cakes have completely cooled in the refrigerator before cutting the layers; moist cakes like this one are easier to handle when fully chilled. Cut each cake in half horizontally to make two layers.
Place the first layer of cake on a 20.5cm (8”) round cake board, holding it in place with a smear of buttercream underneath. Spread one third of the cream cheese filling on top and continue to stack and fill the carrot cakes, ending with the fourth layer of cake.
Crumb-coating helps seal the cake crumbs into the cake so they don’t get stuck in the cake covering. To crumb-coat the cake, spread a thin layer of buttercream over the top and sides with a palette knife, using a cake scraper to neaten the surface where necessary. Use the cake board as a guide when applying the buttercream so the cake does not become larger than the board. If you would like to add two coats of buttercream for a neater finish, refrigerate the cake between coats.
Refrigerate the cake for 30 minutes or freeze it for 10 minutes before covering it with sugar paste or another covering of your choice.