Preheat oven to 160 C (320F). Line a standard loaf tin and line with baking paper. Set aside. As this recipe takes over 1 hour to cook it is best to know your oven temperature- you can test this with a store-bought oven thermometer. If your oven is hotter than 160C (320F) you will have an un-cooked centre.

Add butter to a small saucepan and melt gently over low heat. Turn off heat and set aside to cool for 5 minutes.

Sift almond meal, arrowroot, coconut flour, baking powder, salt and cinnamon into a large mixing bowl and mix until uniform. Set aside.

In a second bowl, add eggs, grated apple, vanilla, the melted and cooled butter and coconut sugar. Mix well, then pour this wet mix into the dry mix and gently fold to combine. Mix until all the dry pockets of flour have gone then gently transfer to your prepared loaf tin. The batter will be very thick- this is normal- use a clean spoon to even it out. Decorate with sliced apple if leaving off the frosting.

Bake for 1 hour 10 minutes to 1 hour 20 minutes, or until cooked through when tested with a skewer in the centre. There should be no wet batter when tested, but some moist crumbs are. Allow to cool for 10 minutes in the pan before gently transferring to a wire rack to cool completely. DO NOT cut up while still warm. If you MUST HAVE warm cake use a very sharp knife to slice the cake, being careful to avoid squishing it.

If making the frosting make sure the cake has completely cooled first. Add butter to a saucepan and melt over low heat. Continue to simmer on low heat, stirring, for 3-4 minutes or until the butter starts to brown. Turn off heat and immediately transfer to a bowl. Add remaining ingredients and whisk together until smooth, then set aside until the frosting has thickened and is a spreadable consistency. Once cake has completely cooled spread on top and serve.