Heat the oil in a large pot over medium heat. Add the onion and sauté for 5 minutes, or until translucent.
Reduce the heat to medium-low. Add the barley, garlic, and thyme and sauté for 3 minutes.
Stir in the mushrooms. Add the broth, tomato paste, vinegar, bay leaf, and salt and stir to combine. Bring the soup to a boil. Reduce the heat to low, cover, and simmer for at least an hour, or until the barley is tender.
Remove the bay leaf. Season to taste with more salt, if desired, and black pepper.