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Cut the chuck roast into 4 - 6 chunks and season all over with the salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Sear the beef until browned and crispy, 3 - 5 minutes per side.
Pour the red wine over the beef and simmer until the wine is reduced by half.
Meanwhile, add the garlic, carrots, celery, onion, tomato paste, crushed tomatoes, and beef broth to the crockpot and stir to combine.
Nestle the beef into the sauce, then pour in the reduced wine and any pan juices. Add the thyme and bay leaves.
Cover and cook on LOW for 8 - 10 hours or HIGH for 4 - 5 hours.
Transfer the beef to a plate and discard the thyme stems and bay leaves. Shred the beef into small pieces.
Return the beef to the crockpot. Stir in the coconut milk or cream, if using.
Cook on LOW, uncovered, for 10 - 20 minutes, until the sauce thickens. Season to taste with salt.
Meanwhile, cook the tagliatelle in a large pot of salted boiling water until al dente. Reserve ½ cup of pasta water, then drain and return the pasta to the pot.
Toss the pasta with the ragu, adding the reserved pasta water a splash at a time for a thinner sauce. Serve topped with parmesan.