Heat 4 quarts high-heat oil in a large stockpot (make sure there is plenty of room between the oil and the top of the pot, as it will bubble up when you add the onion) over medium-high heat until 375ºF. Meanwhile, prepare the breading and cut the onion.
Place 1 cup all-purpose flour, 1 tablespoon paprika, 2 ½ teaspoons of the kosher salt, ¾ teaspoon cayenne pepper, 1 teaspoon dried oregano, ¾ teaspoon ground cumin, ¾ teaspoon garlic powder, and ½ teaspoon black pepper in a large bowl and whisk to combine. Remove and set aside about ¾ cup (does not need to be exact) of the flour mixture; keep the remaining in the bowl.
Place 2 large eggs, ½ cup buttermilk or milk, and the remaining ¼ teaspoon kosher salt in a medium bowl and whisk to combine.
Using a sharp chef’s knife, trim ½ to ¾ inch of the stem end (opposite of root end) from 1 large sweet onion and peel away the outer skin. Place the onion root-side up on the cutting board.
Insert the tip of the knife about ½ inch below the root and cut down towards the cutting board. Do not make back-and-forth slicing motions; this will rip the petals. Spin the onion clockwise a quarter turn and repeat the cut. Repeat turning and cutting twice more.
Avoiding the root again, make 4 more cuts between the first 4 cuts so that there are now 8 sections but the root is still intact. Make 8 more cuts between the first two rounds of cuts so that you now have 16 sections but the root is still intact.
Flip the onion over to reveal the cuts and spread them to open like a flower. If there are any stuck pieces in the center, use the tip of your knife to slice to release (if you don’t do this, you may have raw onion in the center).
Place the onion cut side up into the flour mixture. Sprinkle the reserved flour over the onion, making sure to spread the petals so the flour gets in all the nooks. Dust off any excess flour.
Gently transfer the onion into the egg mixture, cut side down. In a scooping motion, lift up and spread the petals to coat completely in the egg. Scoop out some of the flour mixture into the measuring cup again, leaving some still in the bowl. Transfer the dipped onion, letting the excess liquid mixture drip back into the bowl, into the flour mixture cut side up. Spread the petals and sprinkle with the reserved flour mixture section by section so all the petals are well coated on all sides.
Line a baking sheet with a wire rack and top with a paper towel.
When the oil is ready, place the breaded onion in a spider cut-side up. Carefully lower into the oil (be careful, it will bubble up). The oil temperature will drop, so adjust the heat as needed to keep it between 360 to 365ºF. Fry until deep golden brown on the bottom, about 4 minutes. Flip the onion and fry until deep golden brown and knife tender, 3 to 4 minutes more.
Using the spider, pick up the onion out of the oil cut side down and let the excess oil drip back into the pot. Place cut-side up on the paper towels. Sprinkle with the remaining ¼ teaspoon kosher salt. Let cool about 5 minutes before serving with dipping sauce if desired.