In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic, sliced mushrooms, and cauliflower florets to the pot. Sautéfor another 5-7 minutes, until the mushrooms release their moisture and start to brown slightly.
Stir in the sweet potato cubes, ground cumin, smoked paprika, dried thyme, salt, and pepper. Cook for another 2 minutes, allowing the spices to become fragrant.
Pour in the vegetable broth, ensuring that all the vegetables are submerged. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 20-25 minutes, or until the sweet potatoes and cauliflower are tender.
Using an immersion blender or a regular blender, carefully puree the soup until smooth and creamy. If using a regular blender, be sure to blend in batches and allow the soup to cool slightly before blending.
Return the blended soup to the pot over low heat. Stir in the coconut milk and let it simmer for an additional 5 minutes to heat through.
Taste and adjust the seasoning with more salt and pepper if needed.
Serve hot, garnished with fresh parsley or chives if desired.