To prepare the dipping sauce: In a small mixing bowl, blend together mayonnaise, horseradish, ketchup, paprika, salt, black pepper, and a pinch of cayenne pepper. Then keep it in the refrigerator until you are prepared to serve.
Prepare blooming onion: In a deep bowl large enough to hold an onion, whisk together milk and egg. In a separate bowl, mix together flour, salt, cayenne pepper, black pepper, garlic powder, thyme, oregano, and cumin until thoroughly combined.
To prepare an onion, start by cutting 3/4 inch off both the top and bottom, then peel away the skin. Next, remove a 1-inch diameter core from the center. To slice an onion into 16 sections, start by using a sharp and large knife to make a cut down the center of the onion, stopping 3/4 of the way down. Then, rotate the onion by 90 degrees and make another slice. Feel free to repeat the process of dividing each section in half until you end up with a total of 16 sections. Take care not to cut through the base of the onion while slicing.
Separate the petals, dip them in the milk mixture, and then thoroughly coat them with the flour mixture. Repeat the process by separating the petals once more and dusting them with the flour mixture, followed by another dip in the milk mixture and a final coating in the flour mixture. Place the battered onion in the refrigerator for a minimum of 15 minutes as you preheat the oil.
Add sufficient oil to fully immerse the onion in a deep fryer or deep pot. Heat the oil to a temperature of 350°F (175°C).
Fry the onion with its right side facing up in hot oil until it turns golden brown, which should take approximately 10 minutes. Once finished, take the onion out and place it on a rack or on paper towels to allow it to drain.
Create a wide opening in the center of the onion to accommodate the dipping sauce bowl and serve while warm.