Preheat the oven to 180C/350F/Gas 4.
Season the pork cheeks, to taste, with salt and freshly ground black pepper.
Heat one tablespoon of the olive oil in a non-reactive frying pan over a medium heat, and fry the pork cheeks for 4-5 minutes, or until browned on all sides. Remove the pork from the pan and set aside.
Carefully drain the fat from the pan add the vinegar, scraping up any browned bits with a wooden spoon to deglaze. Remove from the heat.
Heat the remaining olive oil in a frying pan and fry the onions and carrots for 2-3 minutes, or until softened.
Add the white wine and spices and continue to cook until the volume of the mixture has reduced by half.
Place the pork cheeks and pan juices into the pan and add the remaining pork cheek ingredients. Bring the mixture to the boil, then transfer to the oven to cook for 1½-2 hours, or until the pork cheeks are tender.
Remove the pork cheeks from the pan and set aside, then strain the cooking mixture through a sieve. Reserve the liquid and discard the vegetables.
Cook the pork cheeks and reserved cooking liquid in a saucepan for 4-5 minutes, or until the liquid has reduced slightly and the pork cheeks are sticky and glazed.
Meanwhile, for the polenta, heat the milk and stock in a saucepan and bring to the boil. Slowly whisk in the polenta and simmer for 4-5 minutes.
Stir in the parmesan and butter and season, to taste, with salt and freshly ground black pepper.
To serve, heat the butter in a frying pan and fry the kale for 4-5 minutes, or until wilted and tender. Heat the olive oil in a frying pan and fry the squid for 1-2 minutes, or until just cooked. Season, to taste, with lemon juice and salt and freshly ground black pepper.
Spoon some polenta onto each of 4 serving plates, top with the pork cheeks and squid and spoon the kale alongside.