Prep the beef. Preheat the oven to 300°F. Pat the beef shanks dry and season both sides with 1 teaspoon salt and ½ teaspoon pepper. In a shallow dish, combine the flour with the remaining 1 teaspoon salt and ½ teaspoon pepper. Lightly coat the beef in the flour, shaking off any excess.
Cook the pancetta. Add the pancetta to a large Dutch oven over medium heat. Cook, stirring occasionally, until the fat renders and the pancetta is lightly crisp, about 5–7 minutes. Transfer to a plate, leaving the drippings in the pot.
Brown the beef. Increase the heat to medium-high. Add 2 tablespoons olive oil and 2tbsp butter. Sear the beef in batches for 3–4 minutes per side, until browned. Transfer to a plate.
Cook the vegetables. Reduce the heat to medium. Add the onion, carrots, and celery. Cook for 7–10 minutes, stirring occasionally, until softened. Add the garlic and cook for 1 minute.
Build the sauce. Stir in the tomato paste and cook for 2–3 minutes. Pour in the wine, scraping up the browned bits from the bottom of the pot. Simmer for 5 minutes.
Add the beef and liquid. Stir in the tomatoes, passata, and beef broth. Return the beef and pancetta to the pot, along with any resting juices. The liquid should reach most of the way up the shanks; add more broth only if needed. Tuck in the bay leaf, rosemary, thyme, and Parmesan rind, if using.
Braise until tender. Bring to a gentle simmer, cover tightly, and transfer to the oven. Cook for 3–3½ hours, checking at 3 hours. The beef should pull apart easily with a fork. If it’s still firm, cover and continue cooking in 30-minute increments, adding a splash of broth if needed.
Shred the beef. Transfer the shanks to a plate. Remove the bay leaf, herb stems, and Parmesan rind from the sauce. Shred the beef, discarding the bones and any tough connective tissue.
Finish the sauce. Skim off excess fat from the surface. If the sauce is thinner than you’d like, simmer uncovered on the stovetop for 10–15 minutes to reduce. Return the shredded beef to the pot and season with salt and pepper to taste.
Serve. Toss with cooked pasta, adding a splash of pasta water as needed to help the sauce coat the noodles, or spoon over creamy polenta. Finish with freshly grated Parmigiano Reggiano and enjoy!