Trim the top 1/2 inch off the onion and peel the outer skin, leaving the root end intact. Cut a small sliver off the root if necessary to ensure it sits flat, but do not remove the root core.
Place the onion root-side up on a cutting board. Using a sharp chef's knife, make 4 vertical cuts from the root down to the board, stopping 1/2 inch before the root to keep the base connected.
Make 3 additional vertical cuts between each of the 4 initial sections, resulting in 16 total petals. Flip the onion over and gently fan out the petals with your fingers.
In a large bowl, whisk together the flour, paprika, cayenne, garlic powder, oregano, cumin, salt, and black pepper.
In a separate medium bowl, whisk the eggs and milk until fully emulsified.
Place the onion in a clean bowl root-side down. Pour the flour mixture over the onion, using a spoon or your hands to ensure the flour reaches deep between every petal. Turn the onion over and shake off excess flour.
Submerge the floured onion into the egg wash, ensuring every petal is coated. Lift and let the excess liquid drip off.
Return the onion to the flour mixture for a second coating. Ensure the flour adheres to all wet surfaces to create a thick, crispy crust. Chill the breaded onion in the refrigerator for 15 minutes to set the breading.
Heat the vegetable oil in a deep pot or Dutch oven to 375°F (190°C).
Carefully lower the onion into the oil, root-side up. Fry for 3 to 5 minutes. Using a wire skimmer or tongs, carefully flip the onion and fry for an additional 3 to 5 minutes until deep golden brown and crispy.
Remove the onion and drain upside down on a wire rack or paper towels for 2 minutes. Season with an additional pinch of salt while hot and serve immediately with dipping sauce.