Season the beef. Pat the beef ribs very dry, cut any very large pieces into roughly 3-inch chunks, and season all over with the kosher salt and black pepper. For a better crust, do this the night before and leave them uncovered in the fridge.

Sear. Heat the oven to 325 degrees F. Heat the olive oil in a large Dutch oven over medium-high heat. Sear the beef in batches until deeply browned on all sides, about 6 minutes per batch, without crowding the pot. Set it aside and pour off all but about 2 tablespoons of fat.

Build the base. Lower the heat to medium. Add the onions and carrots and cook until soft and golden, about 10 minutes. Add the garlic, tomato paste, and flour and stir for 2 minutes, until the paste darkens.

Deglaze. Pour in the apple cider, scraping up all the browned bits. Simmer for 5 minutes, then whisk in the beef stock and Dijon mustard.

Braise. Return the beef and any juices to the pot with the thyme sprigs. The liquid should come about three-quarters of the way up the meat. Bring to a simmer, cover, and braise in the oven for about 2 1/2 hours. Start checking at 2 hours; it is done when a fork slides in with no resistance.

Finish the sauce. Move the beef to a plate. Skim the fat from the liquid, discard the thyme sprigs, and simmer on the stove until glossy and reduced by about a third, 10 to 15 minutes. Stir in the apple cider vinegar and taste for salt. Return the beef to the sauce to coat it.

Serve. Pile the beef onto plates or a platter, spoon over plenty of sauce, and scatter with fresh parsley. It is delicious over creamy polenta, mashed potatoes, egg noodles, or rice.