Heat olive oil in a soup pot over medium heat. Add shallots, garlic, carrots and celery; cook and stir 2 minutes. Add barley and white wine; cook and stir 2 minutes more. Add mushrooms, thyme, pepper, broth and stock. Bring to boil and reduce heat; simmer 50 minutes.
When barley and vegetables are tender, stir in brie. Cook and stir until brie has melted in to soup. Season to taste with salt and freshly ground black pepper and serve.