01 - Trim the root end just enough so each onion stands upright while staying intact. Peel the onions. Cut 4 to 6 vertical slices from top to root, stopping about ¼ inch from the base so the layers remain connected. Rotate and make additional cuts to form 8 to 12 petals. Gently fan the petals apart with your fingers.
02 - Combine the flour, cornstarch, smoked paprika, garlic powder, onion powder, salt, black pepper, and cayenne in a shallow bowl. In a second bowl, whisk together the eggs and milk until smooth.
03 - Dredge each scored onion in the flour mixture, ensuring all petals are coated. Shake off the excess, then submerge in the egg-milk wash. Return to the flour mixture and press gently to adhere the coating to every petal.
04 - Pour vegetable oil into a deep pot or fryer and bring to 350°F over medium-high heat.
05 - Lower one or two onions into the oil cut-side down. Fry for 2 to 3 minutes until golden, then flip and continue frying for an additional 2 to 3 minutes until the coating is crisp and the onion is cooked through.
06 - Lift the onions out with a slotted spoon and set them on paper towels to drain. Dust with a light sprinkle of salt while still hot if desired.
07 - Stir together the mayonnaise, ketchup, horseradish, smoked paprika, garlic powder, lemon juice, and salt in a small bowl until fully blended.
08 - Arrange the hot mini bloomin onions on a serving plate alongside the dipping sauce.