Heat the olive oil in a Dutch oven over medium-high heat. Add the beef cubes and brown them on all sides, about 5 minutes total. Remove the beef to a plate and set aside.
Lower the heat to medium. Add the onion, carrots, celery, and garlic to the pot. Cook for 4 minutes until the onion softens.
Stir in the flour and cook for 1 minute. Add the mushrooms and cook for 3 minutes until they release some liquid.
Pour in the beef broth while scraping the bottom of the pot. Return the beef to the pot along with the thyme, salt, and pepper. Bring the mixture to a simmer.
Stir in the pearl barley. Cover and cook on low heat for 50 minutes, stirring once or twice, until the beef is tender and the barley is cooked through.