In a large skillet over medium-high heat, add the oil. Sprinkle the short ribs with salt and pepper. When the oil is hot, brown the short ribs, in batches, until they are browned on all sides, 3 to 4 minutes per side. While the short ribs are browning, place a layer of carrot and onion pieces into the bottom of a slow cooker and sprinkle with salt and pepper. Place the browned meat on top. Add the remaining carrots and onions along with the parsnips and turnips. Tie together the rosemary and thyme with the parsley stems, and add them to the pot along with the mustard and Worcestershire. Pour over the stout, and then add enough water to almost cover the contents. Cover and cook on low until the meat is very tender, 6 to 8 hours.
To serve, carefully remove the meat and vegetables from the slow cooker. Strain the juices. Skim off the fat and reserve 2 cups of the juices and 1 short rib for Round 2 Recipe Braised Beef and Mushroom Soup if desired. Serve the rest of the ribs with the remaining juice and garnish with chopped parsley leaves.