Pat the pork cheeks dry and trim away any excess fat or sinew. Season generously with salt and freshly ground black pepper.
Lightly dust the pork cheeks with plain flour, shaking off any excess.
Heat the extra-virgin olive oil in a large, heavy-based pan over medium-high heat. Add the pork cheeks and brown them on all sides, about 4-5 minutes. Remove and set aside.
Finely chop the onions, carrots and garlic. In the same pan, add a little more oil if needed and cook the vegetables over medium-low heat for 10-15 minutes, until softened and lightly golden.
Increase the heat to high and pour in the red wine. Bring to the boil and simmer for 5 minutes, scraping the base of the pan to release any caramelised bits.
Return the pork cheeks to the pan, add the beef stock, bay leaves and thyme sprigs, ensuring the meat is almost covered by the liquid.
Reduce the heat to low. If using a regular pan, cover and simmer gently for 2½–3 hours, or until the cheeks are very tender. If using a pressure cooker, bring to full pressure and cook for 45-60 minutes.
Remove the cheeks and discard the bay leaves and thyme sprigs. Blend the cooked vegetables and cooking liquid with a hand blender until smooth, then return to the pan and reduce the sauce to your desired consistency. Season to taste with salt and freshly ground black pepper.
Add the cheeks back into the sauce, warm through gently and serve piping hot.