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In a large mixing bowl, whisk together the flour, cornstarch, baking powder, and 2 teaspoons of kosher salt until evenly combined.
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Gradually pour in 3 cups of chilled club soda while whisking continuously until the batter becomes smooth. If needed, add a little more club soda, one tablespoon at a time, until the batter reaches the consistency of a thin pancake batter. Let it rest for 10 minutes.
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Pour the vegetable oil into a large, heavy-bottomed saucepan or deep fryer. Heat the oil to 380°F (193°C).
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Separate the onion slices into individual rings. Dip a small batch of onion rings into the batter, allowing any excess batter to drip back into the bowl.
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Carefully place the battered onion rings into the hot oil. Fry for about 3 minutes, turning occasionally, until they become golden brown and crisp.
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Remove the onion rings with a slotted spoon and place them on a paper towel-lined tray to drain excess oil. Sprinkle lightly with salt while still hot.
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Repeat with the remaining onion rings.