Make the sauce: In a medium bowl, combine mayonnaise, ketchup, horseradish, ⅓ tsp paprika, ¼ tsp salt, ⅛ tsp oregano, pinch black pepper, and cayenne. Mix well and refrigerate until serving.
Wet & dry mixes: In one bowl whisk egg + milk. In another bowl combine flour, salt, cayenne, paprika, black pepper, oregano, thyme, and cumin.
Slice onion: Trim top and bottom, remove skin. Cut a 1‑inch core. Slice downward in crosses and subdivisions to create 16 petals, cutting about ¾ down so base stays intact.
Optionally plunge onion into boiling water for 1 minute then cold water to help separate petals.
Double dip: First dip onion in wet mix, then coat with dry mix (sprinkle between petals), then dip again in wet, then again in dry, being thorough.
Fry: Heat oil to ~350°F (175°C) in deep fryer or pot. Place onion upright and fry ~10 minutes until golden.
Drain on rack or paper towels. Gently open petals and place a small dish of dipping sauce in center. Serve immediately.