Place the dried shiitake mushrooms in a bowl and cover with 1 quart of the vegetable stock. Set aside.
Place the cauliflower florets in a medium saucepan and cover with half a quart of the remaining vegetable stock. Bring to a boil over medium high heat, and then turn the heat down to medium low. Cook the cauliflower until it is very soft, about 30 minutes. Set the cooked cauliflower aside (do not drain).
While the cauliflower is simmering, toss the green beans and shallots in 2 Tablespoons of the the olive oil. Spread them out in a single layer on a baking sheet and place the baking sheet in the oven. Roast until crispy, about 20 minutes. Set aside.
Heat the remaining 2 tablespoons of olive oil in a stock pot over medium heat. Add the leeks, garlic and onions and cook, until softened, about 5 minutes. Add the fresh baby bella and shiitake mushrooms and sauté. The mushrooms will release their liquid. Continue to cook the mushrooms until the liquid evaporates, about 10 more minutes.
Pour in the white wine and scrape any brown bits off the bottom of the pan. Add the coconut aminos, soaked dried shiitake mushrooms and the stock you soaked them in. Add the thyme and bay leaves. Stir together to combine and simmer for 30 minutes.
Discard the bay leaves. Transfer the soup to a blender. Pour in the reserved cauliflower and the stock you cooked the cauliflower in. Puree together until smooth.
Return the mixture to the stock pot and heat through. Add the remaining half quart of vegetable stock if the mixture is too thick. Season to taste with the kosher salt and the freshly ground pepper.
Serve hot, garnished with the crispy green beans and shallots.