Heat the oil in a large pot over medium-high heat. Add the mushrooms, carrots, garlic, thyme, and ¾ teaspoon each salt and pepper. Cook, stirring occasionally, until the carrots are tender, 8 to 10 minutes.
Add the vegetable broth and barley. Simmer, partially covered, until the barley is tender, 30 to 35 minutes. Top with the chopped flat-leaf parsley before serving.