To prepare the braised beef: Position the rack in the centre of the oven and preheat the oven to 150C (130C fan). Season the beef with salt and pepper. Heat a heavy medium casserole pot or Dutch oven over medium-high heat. Add 2 tablespoons of the oil, then add the beef and cook, turning as needed, for about 10 minutes, or until the beef is brown on all sides. Remove the beef from the pot and pour off all but 1 tablespoon of the oil.
Add the onion, rosemary, and garlic to the pot and cook, stirring to scrape up the brown bits on the bottom of the pot, for about 8 minutes, or until the onion is golden. Reduce the heat to medium, add the vinegar and then the stock, stirring to scrape up any remaining brown bits. Return the beef to the pot and the water to just cover the meat. Cover the pot and transfer it to the oven. Braise for about 2 hours, or until the meat is almost tender. Transfer the pot the stove top, carefully remove the lid. Increase the oven temperature to 260C (240C fan).
Simmer the beef mixture, uncovered, over medium heat for about 30 minutes, or until the beef is tender and the sauce has reduced to about one quarter of its original volume. Remove the rosemary stems. Season well with salt and pepper.
Meanwhile, to roast the vegetables: On a heavy large baking tray, toss the carrots with the remaining 1 tablespoon oil and season with salt and pepper. Arrange in an even layer over the baking tray and roast for about 10-12 minutes, or until crisp-tender. Toss the carrots with the parsley. Serve the carrots alongside the braised beef and braising liquid.