Sift the flours and bicarbonate of soda into a medium bowl. Combine the water and egg together in a jug then pour into flour mixture. Briefly whisk until almost combined but still lumpy (do not overmix). Stir in the crushed ice.
One-third fill a saucepan or wok with oil and heat over medium heat until hot (a cube of bread should turn golden in 10 seconds).
Dip mushrooms slices 1 at a time, into the batter to evenly coat, allowing excess to drain back into bowl. Drop into the oil and cook in small batches for 3-4 minutes or until batter is light golden. Use a slotted spoon to transfer mushrooms to a wire rack over a lined baking tray. Keep warm in the oven while cooking remaining mushrooms.
Serve with tempura dipping sauce.