In a large Dutch oven or heavy-bottomed pot, heat olive oil and butter over medium-high heat.
Add onion, carrots, and celery. Sauté for 6-7 minutes until vegetables begin to soften.
Stir in garlic and cook for 1 minute until fragrant.
Add all mushrooms and cook for 8-10 minutes, stirring occasionally, until they release their moisture and start to brown.
Stir in the pearl barley, coating it with the vegetable mixture, and cook for 2 minutes.
Add vegetable broth, tomato paste, soy sauce, thyme, bay leaves, and rosemary. Stir well to combine.
Bring to a boil, then reduce heat to low. Cover and simmer for 45-50 minutes, stirring occasionally, until barley is tender.
Remove bay leaves and season with salt and pepper to taste. Stir in fresh parsley and lemon juice just before serving. The stew will thicken beautifully overnight as the barley continues to absorb the broth.