01 - Preheat oven to 350°F.
02 - Season the chuck roast pieces evenly with salt and pepper.
03 - Heat olive oil in a large Dutch oven or heavy ovenproof pot over medium-high heat. Brown the roast on all sides for about 8 minutes, then remove and set aside.
04 - In the same pot, add onion and cook until translucent for 4-5 minutes. Add garlic and sauté for 1 minute.
05 - Stir in crushed tomatoes, tomato paste, beef broth, oregano, basil, chili flakes, and sugar. Bring to a simmer.
06 - Return the browned chuck roast to the pot. Cover tightly and transfer to the oven. Braise for 2 hours, or until the meat is fork-tender and shreds easily.
07 - Cook the pasta in salted boiling water until just al dente. Drain and set aside.
08 - Once the meat is tender, shred it in the pot using two forks. Stir to combine with the sauce. Taste and adjust seasoning if needed.
09 - Increase oven temperature to 400°F.
10 - In a large mixing bowl, toss the cooked pasta with half the sauce and shredded beef mixture.
11 - Transfer half the pasta mixture into a large greased baking dish. Sprinkle with half the mozzarella and Parmesan. Layer the remaining pasta and top with remaining cheese. Spoon extra sauce on top if desired.
12 - Bake uncovered for 20-25 minutes, until cheese is melted and bubbly with golden spots.
13 - Rest for 10 minutes, garnish with chopped parsley, and serve hot.