Trim onion top, leaving root intact. Cut downward into 16 wedges, stopping 1/2 inch above root.

Soak cut-side down in ice water 20 minutes. Drain; blot between petals until dry.

Mix flour, paprika, garlic powder, cayenne, and salt in one bowl. Whisk eggs and milk in another.

Work flour between petals; dip in egg mixture and coat with flour again. Shake off loose powder.

Lower onion cut-side down into 350°F oil. Fry 8 to 10 minutes, turning once, until petals are crisp and deep golden.