Trim the onion top, leave the root intact, and cut downward into 16 wedges that stop 1/2 inch above the root.
Soak the onion cut-side down in ice water for 20 minutes, then drain and blot between the petals until dry.
Mix the flour, paprika, garlic powder, cayenne and salt in one bowl and whisk the eggs with the milk in another.
Work flour between the petals, dip the onion in the egg mixture, coat it with flour again, and shake off loose powder.
Lower the onion cut-side down into 350°F oil and fry for 8 to 10 minutes, turning once, until the petals are crisp and deep golden.