Heat the oven to 200°C (180°C in a fan oven).
Brush the base and sides of the tin with butter and dust with flour, tapping out any excess.
Place the sugar, cinnamon and vanilla in a bowl.
Add the oil, baking powder, flour, coconut, eggs and salt and beat together well.
Stir through the carrots and tip the mixture into the prepared baking tin.
Bake for approx. 45 minutes (cocktail stick test).
Leave to cool in the tin.
For the frosting, beat the cream cheese with the coconut milk, icing sugar and vanilla sugar until smooth.
Whip the cream until stiff and fold in.
Slice the cake into four layers. Place one layer in a cake ring and spread thinly with frosting.
Assemble the remaining layers, spreading each with frosting in the same way, and top with the rest of the frosting.
Chill until ready to serve.
Serve garnished with coconut chips.