Slice 1/2 inch off the top of the onion, peel it, and place it cut-side down. Make 16 cuts from just outside the center down through the onion, stopping 1/2 inch above the root. Flip and gently spread the petals apart.

Mix 3/4 cup flour with the paprika, garlic powder, onion powder, cayenne, salt, black pepper, and oregano. Coat the onion thoroughly with the seasoned flour, working it between the petals, then shake off the excess.

Whisk the remaining 3/4 cup flour with the egg and cold beer until smooth. Coat the floured onion in the batter, working it between the petals. Refrigerate on a rack or plate for 15 minutes.

Stir together the mayonnaise, sour cream, horseradish, ketchup, 1/4 tsp paprika, 1/4 tsp garlic powder, 1/4 tsp salt, and the pinch of cayenne. Cover and refrigerate until serving.

Heat vegetable oil in a large deep pot to 375°F (190°C). Lower the onion in cut-side down and fry for 5 minutes. Flip it cut-side up and fry for another 3 to 4 minutes until deep golden brown.

Drain the onion on a paper-towel-lined plate for 1 minute, then transfer to a serving plate and set the dipping sauce in a ramekin in the center.