In a large pot, heat the olive oil over medium heat. Add the beef stew meat and brown on all sides, about 5-7 minutes. Remove the beef and set aside.
In the same pot, add the diced onion, garlic, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened.
Return the browned beef to the pot. Stir in the rinsed barley, beef broth, diced tomatoes, thyme, rosemary, salt, and pepper.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for about 1 hour, or until the beef is tender and the barley is cooked.
If using, stir in the fresh spinach during the last 5 minutes of cooking until wilted.
Taste and adjust seasoning if necessary before serving.