Soak the leeks in a bowl of cold water to remove any grit. Meanwhile, in a soup pot over medium heat, melt the butter and stir in the rice. Scoop the leeks from the water, shaking off excess, and add them to the pot along with the curry powder, salt, cilantro, and 1 cup of the stock or broth. Cook over medium-low heat at a vigorous simmer for about 12 min, so the rice is almost done. Add the remaining 3 cups stock or broth, the peas, and the spinach and bring to a boil. Boil for about 3 minutes. Turn off the heat and stir in the coconut milk.
In a blender or a food processor, purée the soup in batches until smooth (vent the lid and hold a folded dishtowel over the lid). Taste for salt, season with white pepper, and serve, garnished with fresh cilantro leaves. (If you prefer a soup with more texture, purée 1 cup and return it to the pot, season, garnish, and serve.)