Cook beef stew meat in a large skillet over medium heat until completely browned, 5 to 7 minutes; transfer to a large soup pot.
Heat vegetable oil in the same skillet over medium heat; cook and stir onion, celery, and carrot in the hot oil until the onions are tender, about 5 minutes. Add the vegetable mixture to the beef in the pot.
Pour beef stock into the pot.
Stir pearl barley into the stock.
Place soup over medium-low heat, bring to a simmer, and cook, stirring occasionally, until the beef is completely tender, about 2 hours.
Stir mushrooms through the soup; cook 1 hour more.