Preheat the oven to 180°C (350°F) (160°C/325°F fan-forced).
Add the onion, carrot, celery, garlic, tomato paste, passata, beef stock, oregano, thyme and bay leaves directly to a large, deep ovenproof casserole dish with a lid. Stir until well combined.
Season the beef all over with the salt and pepper, then drizzle with the olive oil. Arrange the two pieces of beef on top of the ragu mixture. Don’t push them down into the sauce.
Place a sheet of baking (parchment) paper over the beef and sauce, pressing it gently down so it sits close to the surface, then cover with the lid. Bake for 1½ hours. Turn the beef pieces over, replace the baking paper, then cover again with the lid and cook for a further 1½ hours.
Check whether the beef pulls apart easily with two forks. If it is still firm, cover and continue cooking for another 20–30 minutes at a time, until completely fall-apart tender.
Remove and discard the bay leaves. Shred the beef directly in the casserole dish using two forks, discarding any large pieces of fat, then stir the shredded beef through the vegetables and tomato sauce.
Add 125 ml (½ cup) of the additional beef stock and stir well. Add more, a little at a time, if needed.
Increase the oven temperature to 200°C (400°F) (180°C/350°F fan-forced). Tear or cut the fresh lasagne sheets into large pieces, roughly 8–10 cm (3¼–4 inches). Using tongs, tuck the pieces randomly throughout the beef ragu.
Scatter the mozzarella evenly over the top.
Bake, uncovered, for 20–25 minutes, or until the lasagne sheets are tender and the mozzarella is bubbling and golden.
Allow the lasagne to rest for 10 minutes. Finish with the parmesan and fresh basil, then serve.
