Heat large deep pot over high heat. Add half the ground beef; cook, using wooden spoon to break up meat into bite-size chunks and gently stirring occasionally, about 10 minutes or until liquid evaporated and beef is well browned. Push beef to one side of pot, tilt pot; spoon off excess fat. Scoop beef into medium bowl; set aside. Repeat with remaining beef, leaving about 1 tsp (5 mL) fat in pot; add beef to bowl.
Meanwhile, cut carrots crosswise into ¾-inch (2 cm) thick slices, cutting thick ends in half. Cut each potato into 6 chunks.
Add onion, 1 tsp (5 mL) salt and ½ tsp (2 mL) pepper to pot; cook, stirring, for 3 minutes or until onion is soft and lightly browned. Add garlic and thyme; cook, stirring, for 30 seconds. Sprinkle with flour; cook, stirring, for 1 minute.
Gradually stir in broth; add vinegar and mustard. Stir in carrots and potatoes. Bring to boil, scraping up bits stuck to pot. Stir in beef. Cover, leaving lid slightly ajar. Reduce heat; boil gently for 15 minutes, stirring occasionally, until potatoes start to soften.
Meanwhile, cut parsnips crosswise into ¾-inch (2 cm) thick slices. Stir into stew, cover with lid ajar; boil gently for about 10 minutes or until vegetables are tender. Season to taste with salt and pepper.
Ladle into bowls; garnish with parsley and serve with ketchup, barbecue sauce or steak sauce (if using).
