Arrange oven rack in upper third of oven and preheat oven to 425°F
Brush oil onto bottom and up sides of an 8-inch baking dish to thoroughly coat inside dish. Arrange cut-up pieces of hot dog in dish and bake for 5 minutes.
In a medium bowl, combine flour, milk, egg and 2 Tbsp. water; season with salt and pepper and stir thoroughly. Beat using an electric hand mixer or whisk until mixture is completely smooth.
Carefully remove hot dish of hot dogs from oven and pour egg batter on top. Bake for 30 minutes, until puffed and golden brown around edges. Divide into equal portions and serve with warm cheese sauce.