Heat a large pot over medium heat and add the onion and mushroom to the pan. Sauté for 7-8 minutes until the onions turn translucent and starts to brown. Add water 1 to 2 tablespoons at a time, as needed, to keep the vegetables from sticking to the pan.
Add the garlic, thyme, rosemary, and bay leaf, and cook for another minute.
Add the red wine and cook until the wine is reduced by half, about 7-8 minutes.
Add the turnips, potatoes, parsnips, carrots, vegetable broth, tamari, and porcini mushrooms. Bring to a boil. Reduce heat to medium, cover and cook until the vegetables are tender, about 25 minutes. Add water if the stew becomes too thick.
Combine the arrowroot mixture in a small bowl and add it to the stew. Cook until thickened, about 2 minutes.
Season with salt and pepper, and cook for another 5 minutes.