01 - Trim each root end just enough so the onions stand upright without falling apart. Peel completely. Cut 4 to 6 vertical slits from the stem down toward the root, stopping about ¼ inch from the base to keep the layers intact. Rotate and add more cuts to form 8 to 12 evenly spaced petals. Gently pull 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 whole milk until smooth.
03 - Dredge each scored onion in the dry flour mixture, pressing gently to work the coating between the petals. Shake off the loose excess, submerge in the egg-milk wash, then return to the flour mixture and press again to build an even, thorough crust on every petal.
04 - Pour the vegetable oil into a deep pot or fryer and bring to 350°F over medium-high heat. Use a thermometer to maintain a steady temperature throughout frying.
05 - Lower one or two onions at a time into the hot oil, cut side down. Fry for 2 to 3 minutes until the bottom turns golden, then carefully flip and continue frying for another 2 to 3 minutes until the entire onion is deeply golden and crisp all over.
06 - Lift the fried onions out with a slotted spoon and set them on a layer of paper towels to drain. Dust lightly with additional 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 combined.
08 - Arrange the hot mini bloomin onions on a serving plate alongside the dipping sauce. For variety, offer ranch dressing or spicy aioli as additional options.