Place the vegetable oil into a deep, heavy-based saucepan and heat until a small cube of bread sizzles and turns golden when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Place the ice cubes, baking powder and flour into a large bowl and gradually whisk in enough sparkling water to make a batter the consistency of double cream.
Dust the apple slices lightly with flour, shaking off any excess, then dip into the batter.
Carefully place the apple slices into the hot oil and deep fry for 3-4 minutes, or until crisp and golden-brown. Remove from the oil with a slotted spoon and drain on kitchen paper.
In a bowl, mix the sugar and cinnamon together, then sprinkle over the apple fritters. Serve immediately.