Set a heavy-bottomed soup pot over medium-high heat and add the coconut oil. When the oil is hot, add the onions and cook for about 5 minutes, until they just start to brown.
Add the ginger, garlic, turmeric, coriander and cayenne and stir. Add salt, to taste, and stir again. When the soup becomes fragrant (after about 1 minute), add the carrots and water.
Raise the heat and bring to a brisk simmer, then put on the lid and turn the heat to low. Cook until the carrots are tender—about 20 minutes.
While the carrots are cooking, simmer the daikon radish slices in a few inches of salted water until they start to become tender. Drain and set aside.
When the carrots are finished, remove the pot from the heat and let the soup cool slightly. Carefully blend the soup with an immersion blender (or in batches in a regular blender) until the soup is thick and smooth. Place the soup back on the heat and stir occasionally.
In a small pan over medium-high heat, melt 2 more tablespoons of coconut oil. When it’s hot, add the mustard seeds, cumin seeds and serrano. Cook for 1 minute, until the seeds are fragrant and begin to “pop.”
Place the daikon radish in a small serving bowl, add the seeds and pepper and stir. Serve the soup hot and top each bowl with some of the radish mixture and the cilantro. Serve with lime wedges on the side.