Special equipment: a 9-inch springform pan
For the meat sauce: Heat the oil in a large saucepan over medium-high heat. Add the ground meat, a large pinch of salt and a few grinds of pepper. Cook, stirring and breaking up the meat into smaller pieces, until browned, about 5 minutes. Add the onions and cook, stirring frequently, until soft and lightly browned, 8 to 10 minutes. Add the tomato paste, oregano, red pepper flakes and garlic and cook, stirring, until the tomato paste darkens to a brick red, about 1 minute. Add the tomato puree, 3/4 cup water, 1/2 teaspoon salt and a few grinds of pepper. Bring to a high simmer, then adjust to a low simmer. Cover the pan and cook for 30 minutes. (You can make and cool the sauce the day before. Reheat before using the next day.)
For the pasta: Meanwhile, bring a large pot of generously salted water to a boil. Grease a 9-inch springform pan with 1 tablespoon oil. Cook the pasta until slightly less than al dente, about 8 minutes. Drain and toss with the remaining tablespoon oil, then spread out in a single layer on a rimmed baking sheet.
Spread 1/4 cup of the meat sauce on the bottom of the prepared pan. Stand the rigatoni on their ends in the pan until it is completely filled.
For the ricotta filling: Stir together the ricotta, Parmesan, egg, 1 teaspoon salt and a few grinds of pepper. Transfer the filling to a pastry bag or resealable plastic bag, snip off just enough of the tip to make a small opening and pipe into each rigatoni tube. Pipe small mounds of any leftover ricotta mixture on top of the pasta and spread out into a thin layer. (You can cook and fill the pasta the day before.)
Preheat the oven to 375 degrees F. Put the filled springform pan on a foil-lined baking sheet to catch drips. Pour 2 cups of the meat sauce over the pasta, spreading it with the back of a spoon so that it drips in between the noodles. Top with the mozzarella and Parmesan.
Cover the pan with foil, doming it slightly to avoid touching the cheese. Bake for 20 minutes. Uncover the pan and continue cooking until the top is golden brown and bubbly, about 30 minutes more. Let the pasta cool for 45 minutes (do not skip this part or your noodles will fall apart when serving!). Sprinkle with parsley, if using, then carefully remove the sides of the pan. Cut the pie into wedges and serve with the reserved meat sauce on the side.
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