
Heat the oil in a large pot over medium-high heat. Add the sliced mushrooms and cook until browned, 10–12 minutes.
Stir in the onion, carrots, and celery, and cook until softened, about 5 minutes.
Add the garlic, tomato paste, thyme, paprika, salt, and black pepper, and cook for 2 minutes, stirring often, until fragrant.
Pour in the broth and soy sauce, then stir in the barley. Bring to a boil, reduce heat, and simmer uncovered for 45–50 minutes, until the barley is tender.