In a medium saucepan, heat the vegetable oil, then saute the onion for 5 to 7 minutes, until tender. Add the corn, water, and potato, and simmer for about 10 minutes, until tender.
Add the milk, salt, and pepper to the saucepan and heat slowly. Do not allow the milk to boil.
With the ladle or measuring cup, remove about 1-1/2 cups of the soup and puree until smooth in a blender. Return to the pot, heat thoroughly, and serve.