Season and flour the beef cheeks, reserving any excess flour.
Heat a sauté pan over a medium heat, add the oil followed by the butter. Once the butter is foaming and golden, add the beef cheeks and colour well on all sides, turning every few minutes until evenly browned. This should take around 15 minutes. Remove the beef from the pan and set aside on a tray.
Add the carrots, celery, garlic and bacon to the same pan and cook for 12–14 minutes until golden. Add the onion and shallots, then season with the sea salt, crushed black pepper, bay leaves and thyme. Continue cooking for around 10 minutes until well caramelised.
Drain off any excess fat, add the reserved flour and cook out for 1 minute. Add the dried mushrooms, red wine, parsley and chicken stock, bringing the mixture to a gentle simmer. Cook for 10 minutes, skimming off any scum that rises.
Return the beef cheeks to the pan, cover with a parchment paper cartouche and a lid, then cook in the oven at 170°C for approximately 2 hours, or until the beef is meltingly tender.
Once cooked, remove the beef from the sauce, place on a tray and shred finely.
Place the sauce over a low heat and reduce to the desired consistency. Pass through a fine sieve twice — first pressing firmly, then a second time gently tapping. Return the sauce to a clean pan, bring to a simmer and skim thoroughly. Thicken lightly with a cornflour and water mix if needed. Add the shredded beef back into the sauce.