Preheat the oven to 375°F (190°C).
Bring a large pot of salted water to a boil. Add the penne pasta and cook until al dente, about 9 minutes. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet. Cook, breaking it up with a spoon, until browned and cooked through, about 7 minutes. Drain excess fat if necessary.
Stir in the crushed tomatoes, tomato paste, dried oregano, dried basil, salt, black pepper, and red pepper flakes. Simmer the sauce for 10 minutes, stirring occasionally.
In a large mixing bowl, combine the cooked pasta and tomato sauce mixture. Stir until pasta is evenly coated.
Add half of the mozzarella cheese and all the ricotta cheese to the pasta mixture. Stir gently to combine.
Transfer half of the pasta mixture into a 9×13-inch baking dish. Sprinkle half of the Parmesan cheese over the layer.
Add the remaining pasta mixture on top and sprinkle with the remaining mozzarella and Parmesan cheeses.
Cover the baking dish tightly with aluminum foil. Refrigerate for up to 24 hours if preparing in advance.
When ready to bake, remove the foil and bake uncovered for 25 minutes.
Return the foil to the dish and bake for an additional 10 minutes to prevent over-browning.
Remove the foil and bake for a final 5 minutes until the cheese is bubbly and golden.
Remove from the oven and let rest for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.