Preheat a soup pot over medium heat. Add the oil and onion. Cook until translucent and beginning to brown, about 5 minutes. Add the garlic and cook for one minute. Add 1 can of coconut milk, 2 cups of water, salt, nutritional yeast, nutmeg and kale. Bring to a simmer. Reduce heat, cover, and simmer 4 to 5 minutes. Uncover and remove from heat. Allow to cool for 5 to 10 minutes.
If you have an immersion blender, use it to puree the soup to the the desired level of creaminess, then add the other can of coconut milk to the pot. Alternatively, pour the other can of coconut milk and about ⅔ of the soup into a blender. **Caution: hot liquids can expand inside a covered blender. Be careful and don't fill the blender more than half full. Start slowly, and vent the top. Work in batches if necessary.** Blend until creamy.
Pour the blended soup back into the soup pot with the unblended portion. Season with black pepper and stir to combine. Serve with vegan cheese and fresh croutons, if desired.
Store leftover cream of kale soup in an airtight container the refrigerator for up to 5 days.