01 - Trim the root end just enough so each onion stands upright without falling apart. Peel away the outer skin. Make 4 to 6 vertical cuts from the top down toward the root, stopping about ¼ inch from the base to keep the layers intact. Rotate the onion and add additional cuts to form 8 to 12 petals, then gently pull them apart with your fingers.
02 - Combine the flour, cornstarch, smoked paprika, garlic powder, onion powder, salt, black pepper, and cayenne pepper in a wide shallow bowl. In a second bowl, whisk together the eggs and whole milk until smooth.
03 - Dredge each scored onion in the flour mixture, turning to coat all petals thoroughly. Shake off the loose excess, submerge in the egg-milk wash, then immediately return to the flour mixture. Press gently to ensure every petal is evenly covered with breading.
04 - Pour vegetable oil into a deep pot or fryer and bring to 350°F over medium-high heat. Use a deep-fry thermometer to maintain a steady temperature.
05 - Lower one or two onions into the hot oil cut-side down. Fry for 2 to 3 minutes until the underside turns golden brown, then carefully flip and continue frying for another 2 to 3 minutes until evenly crisp and cooked through.
06 - Lift the fried onions out with a slotted spoon and set them on a paper towel-lined plate to drain. Season with a light sprinkling of 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 for immediate enjoyment.