Preparation

• Position a rack in the center of the oven, and heat the oven to 400°F.
• Cut the florets from the cauliflower, and discard the core. Coarsely chop the florets, transfer to a food processor, pulse, then process, in batches if necessary, until the cauliflower becomes the consistency of moist, cooked couscous. Spread the cauliflower evenly on a rimmed baking sheet, and bake for 15 minutes, tossing halfway through.
• When cool enough to handle, transfer the cauliflower to a clean kitchen towel, and squeeze until very dry. (You should get 1-1/2 to 2 cups of liquid from the cauliflower; removing as much liquid as possible will give the crust a better texture.)
• Put the cauliflower in a medium bowl. Add 1/2 cup of the mozzarella, the egg, garlic, onion, oregano, 3/4 tsp. salt, and 1/2 tsp. pepper. Mix until well combined. Generously coat a large parchment-lined rimmed baking sheet with the cooking spray. Press the cauliflower dough into two rounds about 3/16 inch thick and 71/2 inches in diameter, being sure to press closed any cracks. Bake until light golden, about 22 minutes, turning halfway through. Remove from the oven, and let cool slightly. Generously coat another piece of parchment with cooking spray. Put the paper coated side down over the crusts. Cover with another large rimmed baking sheet, and flip the crusts over onto the baking sheet. Gently peel off the top parchment, return to the oven, and continue to bake until light golden, turning halfway through, 12 to 14 minutes more.
• Transfer the rack to the top third of the oven. Brush the crusts with the oil. Spread 2 Tbs. of the sauce evenly over each crust, leaving about a 1/2-inch border. Evenly sprinkle the remaining 11/2 cups of mozzarella and the Parmigiano on the crusts, staying within the border. Return to the oven, and bake until the cheese is just melted and bubbly, about 7 minutes. Top with the basil and pepper flakes, and serve immediately.