Pour the vegetable broth into a soup pot, and bring to a boil over medium heat. Stir in the curry powder, cumin, cinnamon, and ginger; add the carrots. Reduce heat to a simmer, and cook until the carrots are tender, about 20 minutes, stirring often.
Strain out the carrots from the broth, and place carrots into a blender, filling the pitcher no more than halfway full. Pour about 1/4 cup vegetable broth into the blender to allow the carrots to puree. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the carrots moving before leaving it on to puree. Puree in batches until smooth, if needed; return the pureed carrots to the vegetable broth. Alternately, you can use a stick blender and puree the carrots right in the cooking pot.
Stir in the coconut milk and the water (use the coconut milk can to measure). Bring back to a simmer; sprinkle with cilantro to serve.
