Begin by preparing your ingredients for the Korean corn dog. Cut the hot dogs and mozzarella cheese into suitable sizes for skewering, ideally around 4-6 inches long. Assemble the wooden skewers by carefully pushing the sharp end into the hot dog and cheese block, making sure they're stable and secure for frying.

In a mixing bowl, combine the all-purpose flour, sugar, and baking powder, whisking them together until evenly mixed. Crack the egg into the bowl, and gradually pour in the milk while stirring. Aim for a smooth, thick batter consistency that can coat your skewered fillings easily.

Prepare your coating station by spreading the panko breadcrumbs on a large plate. If desired, set up any additional toppings, such as crushed ramen or diced potatoes, on separate plates.

Take each skewered filling and dip it generously into the prepared batter, ensuring it's completely coated. Allow any excess batter to drip back into the bowl before rolling in the panko breadcrumbs.

Heat oil in a deep pot to around 160-170°C (320-340°F). Lower each coated skewer into the hot oil, ensuring not to overcrowd the pot. Fry for approximately 3-5 minutes, turning them halfway until they reach a golden-brown color.

Once cooked, remove the corn dogs from the oil and let them drain on paper towels to absorb any excess oil. Immediately sprinkle with caster sugar while they're still hot to add sweetness.