Heat oil in heavy large saucepan over medium heat. Add leeks and 1 tablespoon water; sauté until leeks are tender, about 5 minutes. Add curry powder and stir 30 seconds. Add remaining 2 1/2 cups water, potatoes and salt and bring to boil. Reduce heat, cover and simmer until potatoes are tender, about 10 minutes. Stir in spinach; simmer until just wilted, about 1 minute. Cool slightly.
Working in batches, puree soup in blender until almost smooth. Return soup to same saucepan. Add milk and bring to simmer. Season soup to taste with salt and pepper.
Ladle soup into 4 bowls. Whisk yogurt until smooth. Swirl 2 tablespoons yogurt into each bowl. Sprinkle with cilantro and serve.
