In a large saucepan, cook the ground beef over medium-high heat, breaking it up with a wooden spoon as it starts to brown. Stir in the onion and garlic, lower the heat to medium and cook, stirring occasionally, until the beef is well browned, 12 to 15 minutes.
Stir in the tomatoes and oregano and bring to a simmer over high heat. Stir in the broth, carrots, celery and barley and return to a simmer. Lower the heat and cook until the barley is very tender, about 1 hour. Stir in the parsley; season with salt and pepper.