Pat the chuck roast dry and season with salt and pepper. Sear in hot olive oil in a Dutch oven, about 4 minutes per side, until deeply browned. Remove and set aside.
Add the sliced onions, carrot, celery, and garlic to the same pot. Cook over medium-low heat, stirring occasionally, for 15 minutes until softened.
Pour in the white wine, scraping up the browned bits from the bottom. Stir in the tomato paste.
Return the beef to the pot along with the bay leaf and parmesan rind if using. Add water or broth to come halfway up the beef. Cover and simmer on low, or braise at 325°F (163°C), for about 3 hours, until the onions have fully collapsed and the beef shreds easily.
Remove the beef, shred with two forks, and return it to the pot. Stir in the drained, flaked tuna. Simmer uncovered for 20–25 minutes. Taste and adjust salt.
Cook the pasta until just shy of al dente. Toss directly into the sauce with a splash of pasta water. Serve topped with grated parmesan and fresh basil.