Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery, then cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic and mushrooms. Cook for another 4 minutes until the mushrooms release some liquid and the garlic smells fragrant.
Add the barley, thyme sprigs, vegetable broth, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 minutes until the barley is tender but still chewy.
Remove the thyme sprigs. Ladle the stew into bowls and sprinkle with the chopped parsley before serving.