Add corn, potatoes, water, salt, pepper, and paprika. Bring to a boil; reduce heat to medium; and cook, covered, for about 10 minutes or until potatoes are tender.
Place ½ cup milk in a jar with a tight-fitting lid. Add flour, close lid, and shake vigorously.
Add mixture gradually to cooked vegetables, and then add remaining milk.
Cook, stirring constantly, until mixture comes to a boil and thickens. Serve garnished with chopped fresh parsley.