Slice ½ inch off the top of the onion and peel away the skin, leaving the root end intact. Set root-side down and cut 12 to 16 evenly spaced wedges from top to root, stopping ½ inch above the root on each cut.
Whisk the buttermilk and hot sauce together in a bowl large enough to submerge the onion. Set the onion in cut-side down, then turn root-side down and gently press the petals open. Soak for at least 30 minutes.
Whisk together the flour, cornstarch, paprika, cayenne, garlic powder, onion powder, oregano, salt, and pepper in a large bowl.
Lift the onion from the buttermilk and dredge in the flour mixture, working the flour between every petal. Dip back into the buttermilk for 10 seconds, then dredge in the flour a second time.
Place the dredged onion on a wire rack and refrigerate, uncovered, for 20 minutes.
While the onion chills, whisk together the mayonnaise, ketchup, horseradish, cayenne, paprika, and salt for the dipping sauce. Refrigerate until serving.
Heat at least 3 inches of oil to 350°F in a large pot. Lower the onion in petal-side down, then flip root-side down after 1 minute. Fry for 4 to 6 minutes, until deep golden brown all over.
Lift the onion out and drain root-side down on a wire rack for 2 minutes. Gently pull the outer petals open wider by hand, then serve immediately with the dipping sauce spooned into the center.