Veal cheeks so tender you can eat them with a spoon. (Edward Schneider for The Washington Post)

A few options occurred to me, most immediately a variation on the Belgian beef-and-onion braise, carbonade flamande, which is properly cooked with beer but which I thought would be great with cider. Then the next day at the market, as I was buying milk, I remembered what a friend had told me: The milk folks also sold delicious veal — not the pallid veal of general commerce, but meat from somewhat older calves that had access to grass or forage as well as to milk. This kind of veal used to be despised as indelicate. But “indelicate” often means flavorful.

The guy manning the market stand rummaged around his cooler and offered me a few choices for braising; nothing very tempting, but then he said, “Oh, and I think I’ve got some cheek meat.” Bingo! There were two cheeks in the package, weighing just about a pound, and I’m almost embarrassed to say he charged me only $5.50 for these fine-textured treasures, lean but full of collagen. They’re just the ticket for long, slow cooking.

I hasten to say that any braising cut of veal or pork would be fine in this dish. The texture will, of course, be different, but the point of the cider is its flavor.

From the stand with the best winter vegetables, I bought shallots and Jerusalem artichokes — their sweetness made them good candidates to accompany the braise.

To make it (which I did in the morning but could have done the day before), I heated the oven to 325 degrees. I trimmed the tough connective tissue from the cheeks, seasoned them well with salt and pepper, and browned them until golden in butter; this took a good 10 minutes over heat low enough not to burn the butter. I removed the meat to a plate and sweated a sliced onion and half a small clove of garlic, not sliced, in the same fat; after a minute, I added half a small apple, roughly chopped. I continued to cook this mixture while I ate the other half of the apple, core and all.

Without removing any of the fat (this would happen later), I added the leftover dry hard cider (1 1/2 cups), about 2/3 cup chicken stock (the dish would have been fine without it but less rounded in flavor) and some rosemary — the latter only because I had no sage, which is what I’d have preferred. I boiled this down for 4 or 5 minutes, returned the meat to the pan along with the juices that had accumulated on the plate, laid a circle of parchment paper on top and put the pan into the 325-degree oven, covered but with the lid ajar. (This is a venerable technique newly advocated by Harold McGee, who explains that the temperature in a tightly covered pan will rise to the boiling point — not good for braising.)

I left it alone for three hours — or nearly left it alone. I turned the meat half way through and then checked for tenderness at the three-hour mark by probing the meat with a thin skewer, which met almost no resistance. I removed the pan from the oven and let it cool for 30 minutes or so before taking out the meat, straining the cooking juices and removing the fat from the surface. If the sauce had tasted harsh or poorly balanced, I’d have reduced it and retasted, but it was fine. Better than fine.

In the original braising pan, now washed, I briefly turned some peeled whole shallots in a little butter, then added the sauce and simmered until the shallots were just starting to get tender. At this point, I returned the meat to the pan and set it aside to cool until dinner time.

When we were ready to eat, I reheated the stew (and thus finished cooking the shallots). I might have added some more apple — neatly diced this time — if I’d felt the sauce needed it, but I didn’t. You may feel differently about this. I might have also lightly thickened the sauce with a cornstarch slurry, but didn’t think it necessary — while unthickened, the sauce had built-in body from the veal cheeks.

Served with a mixture of mostly Jerusalem artichokes and a little potato (all simmered in milk and pureed in the food processor with butter and some of the milk), this dish showcased both of its main elements: the gelatinous veal cheeks and the astringent cider (softened by the other ingredients and by long cooking). Mind you, this doesn’t taste like applesauce: Dry hard cider bears the same relation to apples as wine does to grapes or beer to barley. The cheeks’ texture is incomparable — fibrous but not stringy. We ate ours with spoons, dipping into them as though they were, I don’t know, some kind of dessert. It’s a pity there are only two one-portion cheeks per beast.

At the same time, it was a dish that could have been made with either the cheeks or cider swapped out. Another cut of meat cooked with cider, or the same cut cooked with wine, would still have been delicious.

The beverage of choice would have been more of that cider, but I forgot to put a bottle in the fridge, so we were reduced to white wine. Poor us.