Heat olive oil in a large Dutch oven over medium-high heat. Brown ground beef for 5-7 minutes, breaking it apart with a spoon until no pink remains, then drain excess fat.
Add diced onion, chopped carrots, and celery stalks to the beef, sautéing together for 4 minutes until vegetables begin softening. Stir in minced garlic and cook 1 minute more until fragrant.
Pour in beef broth and add pearl barley, stirring well to combine. Add diced tomatoes, bay leaves, thyme, oregano, salt, and pepper to the pot.
Bring the hearty savory beef barley soup to a rolling boil, then reduce heat to low and simmer covered for 35-40 minutes. Stir occasionally to ensure barley cooks evenly.
Add diced potatoes and chopped mushrooms during the last 10 minutes of simmering. Taste and adjust seasonings as needed before serving hot.