Pre-heat the oven to 170°C (340°F) with fan and prepare a large baking tray by lining it with baking paper.
Place a wide-based pan on medium heat without any oil. Add the walnuts and seer them for a few minutes until they start to brown. Keep stirring to prevent them from burning. This will give the walnuts a more intense flavour. Once cooled, chop the walnuts or crush them with a rolling pin.
In a large bowl, add the sugar, eggs, vegetable oil, sour cream (or heavy) and extracts. Whip them up with a hand mixer until properly aerated.
Separately, mix the dry ingredients: flour, salt, baking powder & soda, spices. Whisk them to combine, then add them over the wet ingredients. Use a spatula to fold in the flour, without over-mixing.
Grate the carrots and apple on a fine grater or a food processor. Add them to the batter, along with the chopped walnuts and lemon/orange zest. Use the spatula once again to fold all the ingredients together - do not over-mix.
Pour the batter into the lined baking tray, then smooth it over with a spatula to make it flat. Bake for 20 minutes or until a toothpick comes out clean. Once baked, let it cool down fully in the tray, then cut it in half along the shorter side.
Caramelised walnuts
Place the sugar and water in a small saucepan over medium heat. Cook until an amber colour caramel forms, viscous in texture.
Take the caramel off the heat, then add in the walnuts. Mix well to cover the walnuts in caramel, then carefully transfer the mixture onto a lined baking tray. Try to spread out the walnuts as much as possible with a spatula, then let them cool down for 30 minutes.
Once fully cooled, bread down the chunks of caramelised walnuts and place them in a food processor. Pulse until you obtain a grainy sand-like texture of caramelised walnuts.
Chop the white chocolate into smaller chunks. Melt it in the microwave in small bursts of 15-30 seconds. Let the melted chocolate cool down fully before using it, for approximately 20-30 minutes.
Place the cold butter in a bowl, along with the icing sugar. Whip up the butter using a mixture until it turns creamy. Add in the cream cheese, melted white chocolate and vanilla bean paste. Whip up the mixture until pale and fluffy. Use the cream cheese immediately, without refrigerating it.
Optional carrot decoration: take 2-3 tablespoon of cream and place in 2 separate bowls. Colour one bowl with orange food colour and the other with green.
Assembling the double layer carrot cake
Put the first layer of carrot cake onto platter, then spread the vanilla pastry cream with walnuts onto it. Level out the cream with a spatula to make it even throughout.
Add the second layer of carrot cake on top of the vanilla pastry cream. Put the cream cheese frosting on top, spreading it evenly with a spatula or knife. Sprinkle the remaining caramelised walnut on top. Chill the cake for a minimum of 2 hours before cutting it to get clean cuts.
Optional carrot decoration: place the orange frosting in a piping bag fitted with round 1 cm (½ inch) nozzle. Place the green frosting in a piping bag fitted with a small star nozzle. Pipe dollops of the orange frosting on top of the carrot cake to resemble carrots. Pipe the green carrot leaves on top.
Notes
I recommend using a kitchen scale in grams for more accuracy. The cups used for the conversion are standard US customary cups (1 cup flour = 136g). There are many different types of cups across the globe, which is why I strongly recommend using grams instead.
For best results use an odourless vegetable oil, such as sunflower or rapeseed.
You can use either lemon or orange zest for the carrot cake. Choose according to what you have readily available or personal preference.
In the pastry cream you can also use either only flour or corn starch or both. Get the full detailed information here.
For ease of preparation, you can use cream cheese frosting for both layers. Alternatively, use the pastry cream for both layers. Please note you will need double quantities if you only use one type of filling.