Preheat oven to 375°F. Bring a large pot of salted water to a boil over high. Add ziti, and cook, stirring occasionally, according to package directions for al dente, about 10 minutes. Drain ziti in a colander, and toss with 1 tablespoon of the oil.

While ziti cooks, heat remaining 2 tablespoons oil in a large Dutch oven over medium-high. Break ground beef into medium-sized clumps, and add to Dutch oven. Cook, stirring once halfway through cook time, until deeply browned on 2 sides, 6 to 8 minutes.

Cook, stirring and breaking up meat into smaller pieces with a wooden spoon, until cooked through and no longer pink, about 2 minutes.

Reduce heat to medium. Add onion and garlic, and cook, stirring often, until softened, about 3 minutes.

Stir in plum tomatoes and marinara sauce. Bring to a simmer over medium. Cover, and simmer, stirring occasionally, until slightly thickened, 10 to 12 minutes. Remove from heat, and set aside 3 cups of the ragu.

Add ricotta, cream, salt, crushed red pepper, 2 cups of the mozzarella, and ½ cup of the Parmigiano-Reggiano to remaining ragu in Dutch oven, and stir to combine. Add cooked ziti, and stir until thoroughly combined.

To assemble, spread 1 cup of the reserved ragu in the bottom of a 13- x 9-inch baking dish. Spoon half of the ziti mixture over ragu. Spoon 1 cup of the reserved ragu over ziti mixture. Spoon remaining ziti mixture over ragu. Spread remaining 1 cup reserved ragu over ziti mixture, and sprinkle with remaining 1 cup mozzarella and ¼ cup Parmigiano-Reggiano.

Bake, uncovered, in preheated oven until cheese is melted and browned in spots, 20 to 25 minutes. Let cool 5 minutes. Garnish with parsley.