In a mixing bowl, combine the rice flour, cornstarch, baking powder, and a pinch of salt. Slowly whisk in the soda water a little at a time to achieve a light paste that lightly sticks to the mushrooms and onion when they’re dipped into it.

Pour 2 inches of oil into a 10-inch-wide cast-iron pan or other heavy pan. Over medium to medium-high heat, bring the oil to 360°F. (If you don’t have a thermometer, drop a bit of the batter into the oil: no bubbling means it’s too cool; furious bubbling and smoke means it’s too hot.)

Line a sheet pan with paper towels. Working in batches, dip the mushrooms and onions in the batter to lightly coat, then gently place them one at a time in the oil. Do not overcrowd the pan or the oil will lose its heat. Cook for about 20 seconds, turn over and cook for another 20 seconds, then remove with a slotted spoon and drain on the paper towels.

Repeat with the rest of the mushrooms and onions, sprinkle with salt, and serve immediately.