In a small mixing bowl, combine the mayonnaise, ketchup, creamed horseradish, paprika, salt, oregano, black pepper, and cayenne. Stir until smooth and well blended. Cover and refrigerate for at least 2 hours (preferably overnight) to allow the flavors to develop.

In a medium bowl, mix together the flour, paprika, garlic powder, black pepper, and cayenne. Set aside.

In a large mixing bowl, combine the cornstarch, flour, minced garlic, paprika, salt, and pepper. Gradually pour in the beer while whisking, until a smooth batter forms. The batter should be thick enough to coat the onion evenly but not too heavy.

Slice approximately ¾ inch off the top of each onion (opposite the root). Peel off the outer skin. With the root end intact, make 12 to 16 vertical cuts into the onion, taking care not to cut through the root. Gently spread apart the sections to create a blooming flower shape. For optimal blooming, soak the cut onions in cold water for 1 to 2 hours, then drain and dry thoroughly.

Dredge each prepared onion in the seasoned flour mixture, ensuring all petals are fully coated. Shake off any excess. Dip the floured onion into the beer batter, using a spoon or spatula to ensure the batter reaches between the petals.

Preheat oil in a deep fryer or large heavy-bottomed pot to 375°F (190°C). Carefully lower the battered onion, root-side up, into the oil. Fry for approximately 1½ minutes, then carefully turn the onion and fry for an additional 1½ minutes, or until golden brown and crisp.

Remove the onion from the oil using a slotted spoon or spider strainer. Drain on a paper towel-lined plate. Serve hot with the prepared dipping sauce placed in the center or on the side.