Heat the olive oil in a large pot over medium heat. Add the beef cubes and cook until browned on all sides, about 5 minutes.
Add the onion, carrots, and celery to the pot. Cook for 4 minutes, stirring often, until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute more.
Pour in the low-sodium beef broth. Add the barley, thyme, and black pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 45 minutes, stirring occasionally.
Add the green beans and continue simmering for 15 minutes until the barley is tender and the beef is cooked through.
Remove the pot from the heat. Ladle the stew into bowls and sprinkle with fresh parsley before serving.