If you're set on making an apple rosti you may also be happy to add some potato - which will taste much nicer than you may think. Grate the unpeeled apples coarsely, avoiding core and pips, and squeeze out excess juice but keep the juice. The gratings will turn brown quite quickly but don't worry too much as you're going to fry them anyway and in your case you're topping them with caramel icecream (and might I suggest a dusting of icing sugar as well) so who's going to see it anyway?
Mix the grated apple with an equal amount of grated peeled potatoes, that you've also squeezed out - you can discard the potato liquid. Mix it all together well then add 1 1/2 tablespoons of flour or cornflour per cup of grated mix. You might also like to add some ground cinnamon, allspice, nutmeg or whatever takes your fancy. Mix that all together really well and then begin cooking your rosti.
You can cook them one of several ways. Either form them into compact balls and cook over medium/low heat in small pans to which you've added a tablespoon butter. Once the butter is sizzling add the ball, and press it down flat firmly using the back of a spoon or your fingers if you're brave. The more compact the better the end result.
Once golden on one side, carefully flip over (you may need to loosen it using a small metal spatula - unless you cook in non-stick pans) and cook on the other side till done, adding more butter if it looks like it's drying out. Alternatively, you can cook on one side then carefully flip out on to a baking parchment-lined tray and finish in the oven at 180C. You can also form "patties" and bake on a well buttered tray, brushing each rosti with extra butter but this will be less successful, less likely to have the odd crisp bit that makes a rosti a lovely thing to eat.
Meanwhile, add a few tablespoons of sugar or honey to your apple juice and simmer to make a syrup, which you can then drizzle over the cooked rosti for extra apple-y flavour.
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