In a large bowl, whisk the flour with the cornstarch, baking powder, and the 2 teaspoons of kosher salt. Whisk in 3 cups of the club soda until the batter is smooth. Add more club soda, about 1 tablespoon at a time, until the mixture is the consistency of thin pancake batter. Let stand for 10 minutes.

Meanwhile, in a large saucepan, heat the vegetable oil to 380 degrees. Dip 8 onion rings in the batter, letting the excess drip back into the bowl. Fry the onion rings in the hot oil over high heat, turning occasionally, until golden and crispy, about 3 minutes. Transfer the onion rings to a paper towel-lined baking sheet and sprinkle lightly with salt. Repeat with the remaining onion rings and batter and serve hot or warm.