Sweat the aromatics. In a large pot, warm the coconut oil over medium heat.
Add the onion with a pinch of salt and cook 5–7 minutes until soft and translucent.
Stir in garlic and ginger. Cook 1 minute until fragrant. If using coriander or cumin, add now and toast briefly.
Add carrots and broth. Stir in the sliced carrots and pour in the vegetable broth. Bring to a boil, then reduce to a gentle simmer.
Simmer until tender. Cook 18–22 minutes, or until the carrots are very soft when pierced with a fork.
Blend until smooth. Remove from heat.
Use an immersion blender to puree in the pot, or carefully transfer to a blender in batches. Blend until silky.
Finish with coconut and lime. Return the soup to low heat (if using a blender). Stir in the coconut milk, lime zest, and juice from 1 lime.
Add red pepper flakes if you like a little heat.
Season thoughtfully. Taste and add salt and black pepper. Adjust lime juice to your preference—more for brightness, less for mellow creaminess.
Serve and garnish. Ladle into bowls and top with chopped cilantro, toasted coconut, a swirl of coconut milk, or a tiny drizzle of chili oil for contrast.