01 - Trim and peel each onion, leaving enough of the root intact so onions remain upright. With a sharp knife, make 4 evenly spaced vertical cuts through each onion toward the base, turning and making 4 additional cuts between the previous cuts. Carefully separate the onion 'petals' without detaching the base.
02 - Submerge onions in a bowl of ice water for 10 minutes to encourage petals to open. Remove, drain, and gently pat the onions dry with paper towels.
03 - In a medium mixing bowl, whisk together flour, cornstarch, paprika, garlic powder, onion powder, cayenne pepper, salt, and black pepper until homogenous.
04 - In a separate bowl, beat eggs and whole milk until fully combined.
05 - Dredge each onion in the flour mixture, shaking off excess. Dip into the egg mixture, allowing excess to drip off, then coat a second time in the flour mixture. Gently press the petals to ensure batter adheres throughout.
06 - In a deep fryer or a heavy-bottomed pot, bring vegetable oil to 350°F (175°C).
07 - Working in batches, carefully lower coated onions cut side down into the hot oil. Fry for 2 to 3 minutes, turn to upright, then continue frying another 2 to 3 minutes until golden and crisp on all sides. Transfer fried onions to paper towels to drain excess oil.
08 - Combine mayonnaise, ketchup, horseradish, smoked paprika, garlic powder, salt, and black pepper in a bowl. Mix thoroughly until smooth and uniform.
09 - Arrange fried onions on a platter and serve warm with the prepared dipping sauce.