Soak onion rings in a bowl of ice water for 1 hour; drain and pat dry with paper towels.
Whisk 1 cup plus 2 tablespoons flour, milk, egg, 2 tablespoons vegetable oil, and salt together in a bowl until smooth.
Heat oil in a deep fryer or large saucepan to 375 degrees F (190 degrees C).
Working in batches, dip onion rings in batter until evenly coated; arrange in a single layer on a plate.
Fry battered onion rings in hot oil in batches, until golden brown and crisp, about 5 minutes; transfer to a paper towel-lined plate to drain.
