Melt coconut oil in a large stockpot over medium-high heat. Add onion and sauté until softened, about 4–5 minutes. Add garlic, ginger, turmeric powder, curry, and harissa or curry paste. Cook for 1 minute, until fragrant.
Add cauliflower and broth, and bring to a simmer. Cover with a lid and cook, stirring occasionally, for about 15–20 minutes, or until cauliflower is tender.
Stir in coconut milk, then remove from heat. Using a hand blender, process until smooth and creamy. Taste and season with salt and pepper if needed.
Sprinkle chili, fresh chopped cilantro and garnish with a few slices of lime. This soup is best served hot.