Heat half the oil in a large shallow casserole over a medium–high heat while you season the beef and dust it in the four. Shake off any excess and add the beef to the casserole in batches, browning it on all sides. Remove from the casserole with a slotted spoon and set aside.
Add the remaining oil to the casserole and fry the onion, carrot, celery and garlic for 5–6 minutes until softened, then add the bay leaves, thyme sprigs and tomato purée. Stir to combine then pour in the wine. Bubble for 2–3 minutes then return the beef to the casserole with the chopped tomatoes and milk. Season well.
Bring to the boil then reduce the heat, cover and simmer gently, for at least 3 hours. Stirring occasionally. The beef should be lovely and tender and give when you push it with the back of a spoon.
When the cooking time is almost up, cook the pasta in boiling salted water according to packet instructions or until al dente then drain and drizzle with extra-virgin olive oil. Shred the meat into the sauce then serve the ragu on top of the pasta, scattered with lots of shavings of Parmesan or pecorino.