Purée garlic, scallions, parsley, thyme, shallots, chile, juice, salt and pepper, and ½ cup water in a blender until smooth; mix with beef in a bowl, cover with plastic wrap, and refrigerate at least 4 hours or overnight.
Remove beef from marinade and dry with paper towels; set aside. Heat oil in a 8-qt. saucepan over medium-high heat. Add beef; cook, turning as needed, until browned, about 8 minutes. Add stock and and bring to a boil; reduce heat to medium, and cook, stirring occasionally, until beef is tender, about 1½ hours. Add carrots, celery, leeks, onion, potatoes, turnips, and cabbage; cook, slightly covered and stirring occasionally, until vegetables are tender, about 20 minutes.
Meanwhile, bring squash and 2 cups water to a boil in a 2-qt. saucepan over high heat; reduce heat to medium-low and cook, covered, until squash is tender, about 10 minutes. Drain, reserving ½ cup cooking liquid and transfer squash and liquid to a blender; purée until smooth and set aside. When vegetables are tender, uncover, and stir in reserved squash purée; cook, stirring occasionally, until soup is slightly thick, 5–10 minutes more; season with salt and pepper and serve with scallions and lime wedges.