01 - Trim each onion root just enough to allow upright standing while keeping the base intact. Peel the outer skin. Make 4 to 6 vertical cuts from stem to root, stopping about ¼ inch from the bottom, then rotate and add cross-cuts to form 8 to 12 petals. Gently pull the layers apart with your fingers.
02 - Combine the flour, cornstarch, smoked paprika, garlic powder, onion powder, salt, black pepper, and cayenne in a wide shallow bowl. In a second bowl, whisk together the eggs and whole milk until uniform.
03 - Dredge each scored onion in the flour mixture, ensuring every petal is well covered. Shake off the loose coating, submerge in the egg wash, then return to the flour mixture and press gently to adhere the breading to all surfaces.
04 - Pour vegetable oil into a deep pot or fryer and bring to 350°F over medium-high heat. Monitor with a thermometer for accuracy.
05 - Lower one or two onions into the oil cut-side down. Fry for 2 to 3 minutes until the underside is golden, then flip and continue frying an additional 2 to 3 minutes until the entire onion is deeply colored and crisp throughout.
06 - Lift each onion from the oil with a slotted spoon and set on paper towels to drain. Dust lightly with extra salt while still hot if desired.
07 - Stir together the mayonnaise, ketchup, prepared horseradish, smoked paprika, garlic powder, lemon juice, and a pinch of salt in a small bowl until fully incorporated.
08 - Arrange the hot mini bloomin onions on a serving platter alongside the dipping sauce. Best enjoyed right out of the fryer while the coating is at maximum crunch.