Prepare the Meat Sauce
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chopped onion along with a generous pinch of salt and a few grinds of black pepper. Sauté until softened and translucent, approximately 5 minutes. Incorporate the ground beef and Italian sausage, breaking them apart with a wooden spoon. Cook until browned and no pink remains, about 8 minutes. Add garlic, tomato paste, oregano, and red pepper flakes (if using), and cook for 1–2 minutes, stirring until fragrant.
Introduce the crushed tomatoes, parsley sprigs, and 1/4 cup water. Stir well to combine. Reduce the heat to medium-low, partially cover with a lid, and simmer for 15 minutes, occasionally stirring, until the sauce thickens slightly. Adjust seasoning with additional salt and pepper as needed. Discard the parsley sprigs once the sauce is complete.
Cook the Pasta
Bring a large pot of salted water to a boil. Cook the mostaccioli according to the package instructions until al dente. Drain thoroughly and toss with a drizzle of olive oil to prevent sticking.
Prepare the Ricotta Mixture
In a medium bowl, combine the ricotta, 1/4 cup Pecorino Romano, the egg, remaining 1/4 teaspoon oregano, a pinch of salt, and a few grinds of black pepper. Mix until smooth and fully incorporated.
Assemble the Dish
Preheat the oven to 350°F (175°C). Lightly grease the bottom and sides of a 9-by-13-inch baking dish with olive oil. Mix the cooked mostaccioli with the meat sauce until well coated. Spread half the pasta mixture evenly into the prepared dish.
Carefully layer the ricotta mixture on top, spreading it evenly with a spatula. Add the remaining pasta mixture over the ricotta. Sprinkle the mozzarella cheese and the remaining 3 tablespoons Pecorino Romano evenly over the top.
Bake
Cover the dish with aluminum foil and bake for 20 minutes, or until thoroughly heated. Remove the foil and continue baking for an additional 10–15 minutes, or until the cheese is fully melted and the edges of the dish are bubbling.
Garnish and Serve
Remove the dish from the oven and let it rest for 5 minutes before serving. Garnish with the chopped parsley. Serve warm.