Preheat oven to 180°C. Line a 20 cm diameter cake tin with baking paper.
Sift the various flours, cream of tartar and baking powder into a large bowl. Add a pinch of salt and stir together using a whisk. Set the bowl to one side.
Wash, peel and cut the apple (or apples) in half. Cut half of the apple into very thin slices of about 1-2 mm thick (a vegetable slicer makes this easy). By using very thinly cut apple slices you avoid any uneven distribution of moisture within the batter. If you like, you can further chop the thin apple slices into tiny cubes. If a whole apple is used for this step, the cake will be moister, yet it will still be light and retain its fresh and airy consistency. If the apple slices are cut too thick, the batter will have a less smooth consistency, and the individual slices of cake will be more likely to crumble during cutting.
Cut the other half of the apple into medium-thick slices of about 3-4 mm and place these slices in a bowl. Spoon over just a little of the orange juice and rice syrup, mix together well using a spatula, and leave to rest (these will be used for decoration).
In another bowl, combine the remaining syrup and orange juice with the peanut oil and the water. Add the grated orange peel, vanilla pod seeds and the thinly cut apple slices; mix together well.
Add the liquid ingredients to the dry ingredients and carefully stir together.
Mix until the batter has a smooth, even consistency and is free of any lumps.
Pour the batter into the cake tin, spreading evenly with a spatula. Decoratively arrange the more thickly sliced apple on top of the batter and lightly press in.
Bake the cake in a preheated oven for 50 minutes or until it is golden and cooked through use a wooden cocktail stick to check that the cake is done. Allow the cake to cool in the oven with the oven door slightly ajar so that the cake doesn't sink in the middle. Moist apple cakes that are baked without eggs have a tendency to collapse, but this apple cake is not overly moist so there should be little danger of this happening. That being said, some apples can be particularly juicy so you should still keep an eye on this. It's best to serve the cake either slightly warm or at room temperature.