Preheat oven to 300 degrees.
In a 5-inch-deep Dutch oven, heat the oil over medium-high heat until very hot but not smoking. Dry the meat with paper towels, sprinkle it generously with salt and pepper, place in the pot, and brown well, about 8 to 10 minutes per side. When the meat is well browned, transfer it to a platter.
Pour off fat or add oil to the pot as needed so you have about 2 tablespoons in the pot. Add the onions and saute, stirring, until translucent, 7 to 9 minutes.
Add the vinegar and bring to a boil, scraping up any brown stuff from the bottom of the pan. Put the meat back in the pot and add the bay leaves, caraway seeds, brown sugar, marjoram, and enough stock so that the liquid comes halfway up the sides of the meat. Bring just to a simmer and skim any scum off the surface then cover, put in the oven, and cook until the beef is fork-tender, 2 1/2 to 3 hours. After 2 hours and 15 minutes, add the apples to the pot; after 2 1/2 hours, remove the apples with a slotted spoon, set aside, and begin checking the meat for doneness. To check for doneness, plunge a fork straight down into the meat and try to pull the fork out. If the fork slides out easily, the meat is done; if the meat hangs on to the fork, give it more time.
When the meat is done, remove it from the pot, cover it loosely with foil, and let it rest for at least 10 minutes. Skim the fat from the braising liquid and taste the liquid. If it needs more flavor, place the pan on the stove over medium-high heat and simmer to reduce the liquid. For a thicker sauce, reduce it until it coats the back of a spoon. Season with salt and pepper. (You can also strain the liquid and pass it and the cooked onions separately.)
Cut the meat into thin slices and serve accompanied by the apples, braising liquid, and onions.