Pour 1/3 cup olive oil into a deep pot, and heat over medium heat. Stir in the carrots, celery, and onion; cook until vegetables can be pierced with a fork, about 5 minutes. Stir in the portobello mushrooms, and cook 5 minutes more. Pour in the chicken broth, and add the parsnips and shiitake mushrooms. Bring the mixture to a boil, then reduce heat to medium, and simmer until the parsnips are soft, about 10 minutes. Remove from the heat.

Place 1/3 cup olive oil in a blender or bowl of a food processor. Add the garlic, tarragon, and thyme, and pulse until well blended. Stir the mixture into the soup. Season to taste with kosher salt.