**Trim the cheeks.** Slide a sharp knife under the tough pearly membrane on one side of each cheek, angle the blade slightly up, pull the membrane taut and cut it away in strips. Discard it.
Pat the cheeks dry, season generously, and dust all over with the flour.
Heat the oil in a heavy casserole over a high heat and brown the cheeks hard on both sides, about 4 minutes a side, in two batches. Set aside.
Turn the heat down to medium. Cook the onion, carrot and celery for 8 minutes, then add the garlic for a minute and the tomato paste for another.
Pour in the red wine and let it bubble hard for 3 minutes, scraping the base of the pan clean.
Return the cheeks, add the stock, thyme, bay leaves and sugar. The liquid should come about three-quarters of the way up the meat. Bring to a simmer.
Cover and transfer to the oven for **3 hours**. Check at 2 1/2 — a fork should slide in and twist with no resistance whatsoever. If there’s any spring left, give it another 30 minutes.
Lift the cheeks out carefully and keep warm. Strain the liquid into a saucepan and boil hard for 10 minutes until reduced by about half and glossy enough to coat a spoon.
Season the sauce, return the cheeks to warm through, and serve over mashed potato with the sauce spooned over.