Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook for 3 to 4 minutes until soft and translucent. Add the minced garlic and cook for another minute until fragrant.

Add the ground beef, breaking it apart with a wooden spoon into small crumbles. Cook for 6 to 8 minutes, stirring frequently, until completely browned with no pink remaining. Drain any excess grease.

Stir in the tomato paste, coating the meat evenly. Cook for 1 to 2 minutes. Add the crushed tomatoes, beef broth, oregano, thyme, salt, and pepper. Stir to combine.

Reduce heat to medium-low and simmer uncovered for 20 to 25 minutes, stirring occasionally, until the sauce is very thick and holds together on a spoon. Remove from heat and let cool for 10 minutes.

While the sauce simmers, bring a large pot of well-salted water to a boil. Cook the rigatoni until just al dente, 1 to 2 minutes less than package directions. Drain and spread on a baking sheet to cool enough to handle.

Preheat oven to 375°F. Transfer the thickened ragu to a piping bag or zip-top bag with one corner cut off. Insert the tip into one end of each rigatoni tube and squeeze gently to fill. Alternatively, use a small spoon to carefully stuff each tube.

Lightly grease a 9x13-inch baking dish. Arrange the stuffed rigatoni in the dish, either laying them flat side-by-side or standing them upright in rows. Pack them snugly so they support each other.

Sprinkle the shredded mozzarella evenly over the top, followed by the grated Parmesan. Bake uncovered for 20 to 25 minutes until the cheese is melted, golden, and bubbling.

Remove from oven and let rest for 5 minutes. Garnish with freshly chopped parsley and serve hot.