Special equipment: a deep-frying thermometer
Slice about 1/4 inch off the top of each onion and slice off just a little bit of the root end, making sure the root is still intact. Peel each onion. Using a paring knife, make a slice from the top of each onion into the center and down to about 1/4 inch above the root. Repeat the cuts going around the onion, spacing them out by 1/3 inch to form the "petals" of the blossom. Once all the cuts have been made, press down on the top of the onion with the palm of your hand to help separate the petals. Repeat with the remaining onions.
Fill a medium heavy-bottomed pot with enough canola oil so it comes up the sides about 3 inches. Heat over medium-high heat to 350 degrees F.
In a pie dish, whisk together the flour, cornmeal, paprika, onion powder, garlic powder and a generous pinch of salt and pepper. In a second pie dish, whisk together the milk and eggs. Working in batches, coat the onions in the egg wash, then dredge in the flour mixture, making sure the onions are coated and the flour mixture gets into all the crevasses of the onion "petals." Place on a plate.
Fry the onions in batches until golden brown, 3 to 4 minutes. Drain on a paper towel-lined plate. Season with a bit more salt. Serve with Onion Blossom Sauce.
Combine the mayonnaise, sour cream, hot sauce, horseradish, paprika, garlic powder and onion powder in a bowl and mix until blended.