Place the shredded apples in a saucepan and let cook for about 5 minutes until you get a half-cooked applecompote. Put aside.
Combine the flour, sugar, baking soda, cinnamon, salt and quatre-épices in a big bowl.
Whisk the oil, melted butter and eggs, add them to the flour-mixture and mix carefully with a spatula until well combined. Add the nuts, carots, the applecompote and coconut and fold them in.
Bake for about 40-50 minutes in 2 buttered 16 cm sized cakepans in the preheated oven at 175°C.
For the frosting mix the cream-chesse and the sugar with an electric whisk for about 3 minutes.
Cut each cake in 2 equal layers. Put a bit of the frosting on each of them, assemble the cake and glaze it with the rest of the frosting.
Sprinkle with shredded coconut.