In a medium bowl, combine mayonnaise, ketchup, horseradish, 1/3 teaspoon paprika, 1/4 teaspoon salt, 1/8 teaspoon oregano, a pinch of ground black pepper and 1/3 teaspoon cayenne pepper; mix well. Keep sauce covered in refrigerator until needed.
For the onions:
To make the batter: In a medium bowl, beat egg and add milk. In a separate bowl, combine flour, 1 1/2 teaspoons salt, 1 1/2 teaspoons cayenne pepper, 1 teaspoon paprika, 1/2 teaspoon ground black pepper, 1/3 teaspoon oregano, thyme and cumin; mix.
To prepare the onion: Slice 1 inch off of the top and bottom and remove the papery skin. Use a thin knife to cut a 1 inch diameter core out of the middle of the onion. Now use a very sharp, large knife to slice the onion several times down the center to create ‘petals’: first slice through the center of the onion to about three-fourths of the way down. Turn the onion 90 degrees and slice it again in an X across the first slice. Keep slicing the sections in half, very carefully until the onion has been cut 16 times. Do not cut down to the bottom of the onion. The last 8 slices will be difficult, be careful.
Spread the ‘petals’ of the onion apart. To help keep them separate, you can plunge the onion into boiling water for 1 minute and then into cold water.
Dip the onion into the milk mixture and then coat it liberally with the flour mixture. Again, separate the petals and sprinkle the dry coating between them. Once you’re sure the onion is well coated, dip it back into the wet mixture and into the dry coating again. This double-dipping ensures you have a well coated onion because some of the coating will come off when you fry it.
Heat oil in a deep fryer or deep pot to 350 degrees F (175 degrees C). Make sure you use enough oil to completely cover the onion.
Fry the onion right side up in the oil for 10 minutes or until it turns brown. When the onion has browned, remove it from the oil and let it drain on a rack or paper towels. Open the onion wider from the center so that you can put a small dish of the dipping sauce in the middle.