Heat vegetable oil in a large casserole pot over medium heat. Add beef brisket joint and cook until browned on all sides, about 2 to 3 minutes per side.
Mix brown sugar, salt, mustard and black pepper together in a small bowl; sprinkle evenly over the roast. Arrange potatoes, carrots and onion in the casserole pot around the roast. Pour vinegar and water over the vegetables.
Place a lid on the pot and cook in preheated oven for about 4 hours, or until the beef is tender.