Prepare slow cooker (or preheat oven to 140°C and use a large casserole dish with a lid).
In a frying pan over medium heat, add two-thirds of the oil, onion, carrot, celery and thyme. Cook, stirring regularly, for 10 minutes or until veges are soft but not coloured. Add garlic and cook for another 2 minutes. Transfer mixture to slow cooker.
Using the same frying pan, heat remaining oil over medium heat. Sear beef cheeks on all sides to brown then transfer to slow cooker. Pour red wine into frying pan to deglaze then add hot water and stock concentrate and mix to combine. Bring to the boil then pour over beef cheeks. Season with green peppercorns (if using, or use salt and pepper). Cook beef cheeks in the crockpot for 6 hours on high (or 4 hours in the oven).
When beef cheeks are cooked, remove from slow cooker and set aside. Transfer cooking liquid to a saucepan, skim fat from the top and bring to the boil. Combine cornflour and cold water and stir through cooking liquid to thicken the sauce. Shred beef cheeks and return to sauce, mixing to combine. Season to taste then gently reheat.
Meanwhile, in a large saucepan of well-salted boiling water, cook pappardelle following packet instructions until al dente (just cooked, still firm to the bite). Drain pappardelle then drizzle a little extra-virgin olive oil over.
To serve, divide pasta evenly among 4 bowls then top with ragù. Finish with shaved parmesan and a sprinkle of parsley.