Preheat the oven to 450 degrees F (230 degrees C).
Cut each hot dog into 6 pieces.
Pour egg, 2 tablespoons vegetable oil, sugar, and milk into a mixing bowl; whisk until combined. Add white vinegar, cornmeal, flour, baking powder, baking soda, kosher salt, and cayenne. Whisk briskly until ingredients are combined and batter is relatively thin and overmixed. Set batter aside for 10 minutes before using.
Meanwhile, brush two 12-cup mini muffin tins with 2 tablespoons vegetable oil. Fill the prepared muffin cups to about 1/8 inch from the top. Gently push a piece of hot dog into the center of each one.
Bake in the preheated oven until nicely browned, about 18 minutes. Let cool for at least 5 minutes before removing from the pan.