Separate onion slices into rings. Soak in cold water for 10 minutes, then drain and pat completely dry.
Whisk buttermilk and egg in one bowl. In a second bowl, mix flour, salt, paprika, and pepper. Place panko in a third bowl.
Dip each onion ring in seasoned flour, then buttermilk mixture, then panko. Set coated rings on a rack for 5 minutes.
Heat 2 inches of neutral oil in a heavy pot to 350°F (175°C). Fry a few rings at a time for 2–3 minutes, turning once, until golden.
Transfer to a rack, season lightly while hot, and let the oil recover to 350°F before the next batch. Serve immediately.