In a medium pan, bring the barley and 4 cups of water to a boil. Cover, reduce heat to medium-low, and simmer until tender, 30 to 40 minutes.
Meanwhile, heat the oil in a large pot over medium-low heat. Add the onions, salt, and pepper. Cover and cook until the onions have softened, 5 to 7 minutes. Add the carrot and celery and cook, covered, for 6 minutes more. Add the mushrooms, increase heat to medium-high, and cook, covered, until they release their juices, about 4 minutes. Add the broth, bay leaves, and thyme and simmer, uncovered, for 10 minutes. Stir in the cooked barley and cook for 5 minutes more. Remove and discard the bay leaves. If desired, season with additional salt and pepper and serve with the sourdough toast.
Tip: If you have a few minutes to spare, bring out the barley's nutty flavor by sauteeing the uncooked grain with 1 tablespoon of olive oil or butter over medium heat for a few minutes before adding the water.