Preheat and Prepare: Preheat oven to 175°C (350°F). Grease and line a cake tin.
Make the Cake Batter: In a bowl, mix sugar, flour, baking powder, baking soda, salt, and spices. In another bowl, whisk sour cream, oil, eggs, vanilla, extract, and zest. Combine both mixtures, then fold in grated carrots, apple, and walnuts.
Bake: Pour batter into the cake tin and bake for 40-45 minutes or until a toothpick inserted in the center comes out clean. Let cool completely.
Caramelize the Walnuts: Heat sugar and water in a saucepan over medium heat until golden brown. Stir in walnuts, coat well, then transfer to parchment paper to cool.
Make the Vanilla Pastry Cream: Heat milk and vanilla in a saucepan. Whisk egg yolks, icing sugar, and cornstarch separately. Gradually pour the hot milk over the egg mixture, whisking constantly. Return to heat and stir until thickened. Remove from heat, add butter, and let cool.
Prepare the Frosting: Melt the white chocolate and let cool slightly. Beat cold butter and cream cheese until smooth, then mix in icing sugar, vanilla, and melted white chocolate.
Assemble the Cake: Slice the cake in half, spread vanilla pastry cream over the bottom layer, then place the second layer on top. Frost with white chocolate cream cheese frosting and garnish with caramelized walnuts.