Fry the pork cheeks on all sides in an oil and butter mixture in a roasting pan. Remove from the roaster and add the onions to the saucepan. Sprinkle with sugar and steam for 5 minutes over medium heat.
Put the pork cheeks back in the roaster. Pour in the cider, add potatoes, carrots, honey and bouquet garni, salt and pepper. Cover and stew on a low heat for 1.5 hours.
After this time add the turnips and cook for another 30 minutes. Take the pork cheeks and vegetables out of the pot and reduce the stew liquid until it is syrupy.
Place the cheeks and vegetables in the sauce and serve warm.