Preheat oven to 320°F. Season the pork cheeks with sea salt and pepper. Dust them lightly with flour, shaking off any excess. In a deep oven-proof pan or casserole, heat 2 tbsp olive oil and brown the pork over high heat evenly on all sides. Remove from the pan and set aside. Lower heat to medium and add the remaining olive oil, diced carrot, celery, onion and garlic and sauté until onion just begins to color, about 5 minutes. Add sherry vinegar and cider, bring to a boil stirring and scraping any brown bits from the bottom of the pan. Reduce heat and simmer for about 2 minutes.
Stir in ginger, paprika, cinnamon, cloves, thyme, bay leaves and season to taste with sea salt and freshly ground pepper. Add apples and pearl onions (if using) and return the pork cheeks with any of their juices back to the pot. Stir well and add just enough stock to almost cover the pork cheeks. Cover with a lid or tightly with foil and put in the oven and cook for 2-3 hours, until the cheeks are super tender and almost falling apart.
Serve pork directly as is with pan juices spooned over the top. Or for something more refined, remove the pork cheeks and pearl onions to a platter or serving plates and strain the remaining pan juices through a fine mesh sieve into a pot and return to the heat to reduce into a rich sauce.
Garnish with fresh thyme and serve with Manchego mashed potatoes, spiced roasted carrots, crusty bread and a Spanish red wine.