01 - Preheat oven to 350°F.
02 - Season chuck roast pieces evenly with salt and pepper.
03 - Heat olive oil in a Dutch oven over medium-high heat. Brown roast on all sides for about 8 minutes, then remove and set aside.
04 - Add onion to the pot and cook until translucent, 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 chuck roast to the pot. Cover tightly and transfer to oven. Braise for 2 hours until meat is fork-tender and shreds easily.
07 - Cook pasta in salted boiling water until al dente. Drain and set aside.
08 - Remove pot from oven. Shred meat using two forks and stir to combine with sauce. Adjust seasoning as needed.
09 - Increase oven temperature to 400°F.
10 - Toss cooked pasta with half the sauce and shredded beef mixture in a large bowl.
11 - Transfer half the pasta mixture to a greased baking dish. Sprinkle with half the mozzarella and Parmesan. Layer 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, bubbly, and golden.
13 - Let rest for 10 minutes. Garnish with chopped parsley and serve hot.