Bring a large pot of water to a boil. Add the cauliflower florets and boil for 7 to 10 minutes, or until fork-tender. Drain and set aside.
While the cauliflower boils, heat the olive oil in a large stockpot or dutch oven over medium-low heat. Add the mushrooms, onion, and thyme. Sauté for about 5 minutes, or until the vegetables just begin to soften, stirring occasionally. Add the garlic and continue to cook for another minute, or until it begins to soften.
Stir in the vegetable broth, increase the heat to medium-high, and bring to a boil. Reduce the heat to low, cover, and simmer for 10 minutes.
Meanwhile, add the boiled cauliflower to a high-speed blender along with the filtered water, cashews, nutritional yeast, lemon juice, and sea salt. Blend on high for two minutes, or until completely smooth and creamy.
Add the cauliflower mixture to the pot of soup and stir to incorporate. Increase the heat to medium and rapidly simmer for just 5 to 8 minutes, to thicken and reduce (keep in mind that it will continue to thicken as it cools).
Taste and generously season with more sea salt and black pepper to taste. (I usually add another 1/2 teaspoon sea salt and lots of freshly ground black pepper, but it will depend on how many mushrooms you add.)
Leftovers can be refrigerated for up to 4 days or frozen for up to 1 month.
If the soup is thicker than desired after refrigerating and reheating, simply whisk in a bit more vegetable broth or filtered water and adjust seasonings as needed.