Preheat your oven to 350°F. Line a rimmed baking sheet with unbleached parchment paper and set it aside.
Rice and cook the cauliflower.
Slice all of the florets off of the cauliflower, rinse them thoroughly, and pulse them in a food processor until they are the texture of short-grain cooked rice.
Place the riced cauliflower in a large, microwave-safe bowl (or a medium, heavy-bottom lidded stockpot), add about 2 tablespoons water and cover tightly with plastic wrap (or the stockpot lid).
Cook on high for 3 to 4 minutes (or over medium heat for about 5 minutes) until the cauliflower is more tender but still firm. Uncover the bowl or stockpot, and allow the cauliflower to cool until no longer hot to the touch.
Drain the cauliflower.
Transfer the cooked and riced cauliflower to a large tea towel or cheese cloth, gather the towel or cloth tightly around the cauliflower and wring out all of the moisture. There will be more moisture than you expect. Keep wringing until the cauliflower is clumped and mostly dry. Set it aside.
Make the fritter mixture.
To a large mixing bowl, add 2 of the 3 eggs and beat well. Add the riced and dried cauliflower, parsley, Parmigiano-Reggiano cheese and Asiago cheese, and mix to combine. The mixture may seem somewhat dry, but will hold together when pressed.
Shape and coat the fritters.
Roll the cauliflower mixture into balls about 1 1/2-inches in diameter, pressing the mixture as firmly together as possible. You should have about 12 balls. Set up a dipping station with three flat bowls.
IIn one bowl, place the cornstarch. In a second, place the remaining egg, beaten with 1 tablespoon water. In the final bowl, place the bread crumbs.
Roll each ball in the cornstarch, then the egg wash, and finally the bread crumbs, and place it on the prepared baking sheet.
Cook the fritters.
Place about 1 inch of oil in a large, heavy-bottom skillet, and place the skillet over medium-low heat.
Once the oil is rippling, press the breaded balls firmly between your palms to create a patty about 1/2-inch thick, and place in the oil. Do not crowd the patties in the oil.
Cook for about 2 minutes on each side, or until lightly golden brown and beginning to firm up. Place each on paper towels to drain briefly, then return to the prepared baking sheet, placing each fritter about 1 inch from the next. Repeat with the remaining fritters.
Place the baking sheet in the center of the preheated oven and bake for 10 minutes, or until beginning to sizzle on the bottom. Remove from the oven, and serve after allowing them to set for about 5 minutes.
Make the dipping sauce.
Combine all of the ingredients in a medium-size bowl and whisk until smooth. Adjust the sauce to taste.
The dipping sauce can be made up to 2 days ahead of time, covered and stored in the refrigerator. Serve at room temperature.