What is a suitable cut of beef for Braising?

I like a good ol’ chuck roast. Just be sure to cook it low and slow.

Chuck or round.

There is another cut he recommends called a 7 blade roast. It’s basically a chuck shoulder cut and can also be found boneless.

Sometimes, depending upon region, they may give it a different name. So, just ask the butcher. He should know what you are talking about.

I was going to suggest crosscut shank, but if they don’s sell short ribs then the chances of beef shank are slim. Veal shank is more common (think osso bucco) but if you can find beef shank, it’s great for braising.
I’m having a hard time believing that the butcher counter at your grocery doesn’t have them. Did you ask or just peruse the ready-packaged shelves? If they get entire sides of beef then they’re there, they just may not put them out. More likely, your large chain grocery is recieving cry-o-vac, processed “large” cuts of beef and then their under-trained, under-paid, “butchers” cut them down into smaller cuts, in which case you should run fleeing from the store as fast as possible.
Hit the specialty shop. I think you’ll be quite surprised that they don’t cost as much as you think. Anyway, you get what you pay for.
That recipe of Alton’s is amazing, btw. Spring for the good stuff.

@breedmitch : I asked. The young man told me they didn’t carry them. He offered x and y but the store isn’t carrying too much “on the bone” cuts any more (probably because the unskilled kids can’t cut it). The ribs I got were more bone than meat, and the recipe proved to be more work than it was worth. I am not a big fan of meat on the bone, but thought I’d try this recipe because it looked good. I won’t eat veal. It’s a non-food item because mom never made it, and I’m not gonna try it now. Plus it may or may not be cruel.

Chuck roast works well, as do beef shanks, round roast, and brisket. These are the more “muscley” parts of the animal and benefit from long, slow cooking breaking down the tough fibers. It doesn’t have to have the bone in it, but the bone and marrow can add a bit to the flavor.