Heat oil in roasting pan or a Dutch oven over medium heat until hot. Add beef brisket; brown on both sides, about 4 minutes per side. Remove brisket; reserve. Add onions, celery and green pepper to the same pan; cook 4 minutes or until crisp and tender, stirring occasionally. Place brisket over vegetables; sprinkle with garlic, dill, bouillon granules, paprika, salt and pepper. Top with bay leaves; spoon half of vegetables from pan over brisket. Add wine and vinegar.
Cover tightly and cook in a 325 degree oven 3 hours. Add potatoes, carrots and parsnips; spoon pan juices over vegetables and brisket. Cover and continue cooking 30 minutes or until vegetables are tender. Carve brisket diagonally across the grain into thin slices; transfer to serving platter with vegetables. Skim and discard fat from pan juices; spoon over brisket and vegetables. Sprinkle with parsley.