Place the hot dogs on the thick, wooden skewers.
If using cheese, cut the hot dogs in half crosswise. Cut the cheese into block pieces as long and thick as the hot dog half. Pierce through the cheese stick with a thin metal skewer or toothpick, then arrange on the wooden skewers with hot dog halves.
Place the prepared skewers with hot dogs and cheese in the refrigerator until ready to coat with the batter.
Place the breadcrumbs or crushed instant ramen noodles on a wide plate.
Pour vegetable oil in a wide saucepan at least 3 inches (7.5 centimeters) deep and place over medium heat to 350˚F (180˚C).
Dip one of the prepared skewers into the rested batter and carefully rotate in one direction to fully cover in an even layer.
Immediately place on the plate of breadcrumbs and turn, pressing gently to coat, until completely covered.
Transfer to the hot oil and cook, turning as needed, until golden brown and heated through, about 4 minutes.
Repeat with remaining skewers, batter, and breadcrumbs.
Serve immediately while still warm with a sprinkling of sugar and a drizzle of ketchup and/or mustard if desired. Careful, the cheese-filled hot dogs will be hot!