Preheat the oven to 400°F.
Toss the cauliflower with 2 tablespoons of olive oil and spread it on a baking sheet. Roast for 15–20 minutes, until golden and nutty.
Meanwhile, heat the remaining olive oil in a large soup pot over medium heat. Add the diced mushrooms, thyme, rosemary, and lemon zest. Cook, stirring frequently, for 5–7 minutes, until mushrooms are browned and fragrant.
Add the shallots, garlic, celery, salt, pepper, and onion powder. Cook for 2–3 minutes, until vegetables are tender.
Stir in the Dijon mustard, miso paste, and tahini until fully incorporated.
Add the mushroom broth, bring to a simmer, then reduce the heat to low. Cover and simmer for 10–15 minutes, until mushrooms are very tender.
While the soup simmers, make the relish by tossing all the relish ingredients together in a bowl. Let sit at room temperature for 15 minutes to allow flavors to meld.
Add the roasted cauliflower to the soup. Blend until smooth using an immersion blender or standing blender.
Stir in the coconut cream and simmer uncovered over medium-low heat until the desired consistency is reached. Adjust seasoning to taste.
Serve hot, topped with a generous spoonful of the mushroom relish.