01 - Peel onions and trim the root end just enough to stabilize. Make 4 evenly spaced vertical cuts downward, leaving the base intact. Rotate and create 4 additional cuts between previous slices. Carefully fan out the petals with your fingers.
02 - Submerge onions in ice water for 10 minutes to promote blooming. Drain thoroughly and pat dry with paper towels.
03 - In a mixing bowl, whisk together flour, cornstarch, paprika, garlic powder, onion powder, cayenne, salt, and black pepper until uniformly combined.
04 - In a separate bowl, beat eggs with whole milk until smooth and homogenous.
05 - Dredge each onion in the seasoned flour mixture, shaking off excess. Dip into the egg-milk mixture, then return to the flour mixture, ensuring all petals are well coated.
06 - In a deep fryer or heavy-bottomed pot, heat vegetable oil to 350°F.
07 - Working in batches, place onions cut side down in the hot oil and fry for 2 to 3 minutes. Turn and fry an additional 2 to 3 minutes, until all surfaces are golden brown and crisp. Transfer to paper towels to drain.
08 - In a small bowl, blend mayonnaise, ketchup, prepared horseradish, smoked paprika, garlic powder, salt, and black pepper until smooth.
09 - Present the hot onions with accompanying dipping sauce for immediate enjoyment.