Season chuck roast all over with salt and pepper. Heat 1 tablespoon olive oil in a large pot over medium-high heat until shimmery. Work in batches to avoid overcrowding the pan and brown beef on all sides, about 5 minutes. Transfer to slow cooker.
Reduce heat to medium-low and add remaining 1 tablespoon olive oil to the pot. Sauté onion, carrot, and celery until soft, scraping up brown bits, about 5 minutes. Stir in garlic and cook until fragrant.
Pour vegetables on top of meat along with tomatoes, ¼ cup water, bay leaves, thyme, and ½ teaspoon salt and pepper.
Cover and cook on low for 6-8 hours or high for 2-3 hours.
When beef is cooked, transfer to a plate and use two forks to finely shred the meat, discarding herb stems and bay leaves. Keep beef and leftover sauce warm.
Bring a large pot of salted water to a boil. Cook pasta according to package directions. Drain, reserving ½ cup cooking water. Return pasta to pot, along with butter, parmesan, half of the ragu sauce, and half the beef. Cook over medium heat for 1-2 minutes, gently tossing pasta until butter is melted and noodles are coated in sauce. Add a splash of reserved cooking water if needed to loosen the sauce. Taste and stir in more ragu sauce, if desired.
To serve, scoop a portion of pasta into a bowl and top with extra beef and parmesan. Serve immediately.
Instant Pot directions: Use Instant Pot’s “Sauté” setting to brown the beef and cook the vegetables according to Steps 1-3, transferring beef to a plate when needed. Secure the lid and close the pressure valve. Cook on manual for 40 minutes at high pressure then let the pressure naturally release for 20 more minutes. Remove the lid. Continue with the recipe in step 5.