Heat 4 quarts high-heat oil in a large stockpot 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 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 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.
Trim ½ to ¾ inch of the stem end from the 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. Spin the onion clockwise a quarter turn and repeat the cut. Make 4 more cuts between the first 4 cuts to create 8 sections without cutting through the root.
Make 8 more cuts between the first two rounds of cuts for 16 sections, keeping the root intact.
Flip the onion over to reveal the cuts and spread them to open like a flower. Use the tip of your knife to slice any stuck pieces in the center.
Place the onion cut side up into the flour mixture. Sprinkle the reserved flour over the onion, ensuring it gets into all sections.
Transfer the onion into the egg mixture cut side down, lifting and spreading the petals to coat. Then, transfer it back into the flour mixture, ensuring all petals are well coated.
Line a baking sheet with a wire rack and place a paper towel on top.
When the oil is ready, carefully lower in the breaded onion cut-side up. Fry until deep golden brown on the bottom, about 4 minutes, then flip and fry until golden brown and knife tender, about 3 to 4 more minutes.
Remove the onion from the oil using a spider and let excess oil drip back into the pot. Place cut-side up on paper towels and sprinkle with remaining kosher salt. Let cool for 5 minutes before serving with dipping sauce if desired.