Warm the olive oil in a large pot over medium heat.
Sauté onion, carrot, and celery with a pinch of salt until softened, 5–7 minutes.
Stir in mushrooms and cook until they release liquid and begin to brown, about 8–10 minutes.
Add garlic, thyme, and smoked paprika; cook 1 minute until fragrant. Stir in tomato paste and toast 1 minute.
Pour in vegetable broth. Add barley and soy sauce. Bring to a boil, then reduce to a gentle simmer.
Cover partially and simmer, stirring occasionally, until barley is tender, 40–45 minutes.
Season with pepper and salt. Stir in lemon juice and parsley. Rest 5 minutes before serving.