Heat the oil in a pot on medium heat. Sauté the onion and celery until tender for about 5 minutes.
Add the corn and chicken broth. Season with salt and pepper, the bring to a low simmer, partially covered with a lid for about 30 minutes. Add in the milk and bring back to a simmer.
Slowly stir in the flour/water mixture and simmer until the soup is creamy and thick. Taste and adjust any seasonings with salt and pepper to taste. Serve with crackers. Garnish with parsley.