Place onions in a large bowl filled with cold water and soak 10 minutes.

Heat 2 inches of oil in a deep, heavy-bottomed pot to 365 degrees.

In a medium bowl, whisk together flour, cornstarch, baking powder, and salt.

Whisk in ice-cold water and place batter bowl over a bowl of ice.

Drain white onions and dry thoroughly between layers of paper towels.

Working one handful at a time, dip onions in batter, allowing excess to drip back into bowl, and gently place in oil.

Fry, turning once, until crisp and golden, 3 minutes.

Transfer to a paper towel-lined tray to drain and sprinkle with salt to taste.

Serve with mayo-ketchup dip.