Cut each hot dog into four bite-size pieces. Pat them very dry with a paper towel, because moisture makes the batter slide off. Push a toothpick or short skewer into each piece and set them aside.
Add the flour, cornmeal, sugar, baking powder, and salt to a large bowl. Whisk them together until the mixture looks even. This keeps the baking powder spread out, so every bite puffs up the same way.
Crack the egg into the bowl and pour in the milk. Whisk until the batter is smooth and thick, like pancake batter. If it feels too stiff, add a splash of milk, and pour it into a tall glass for easy dipping.
Pour the oil into a heavy pot until it is about 2 inches deep. Heat it over medium heat until it reaches 350°F on your thermometer. Wait for the right temperature, because cold oil makes greasy corn dogs.
Hold a skewer and dip one hot dog piece into the batter. Turn it slowly so it is fully coated, then let the extra batter drip off. A thin, even layer cooks faster and looks neater.
Lower three or four pieces into the hot oil at a time. Fry them for about 2 to 3 minutes, turning once, until they are deep golden brown. Do not crowd the pot, since that drops the oil temperature fast.
Lift the corn dogs out with a slotted spoon and set them on a paper towel-lined plate. Let them rest for a minute or two. The inside is very hot, so give them a moment before you serve.
Arrange the mini corn dogs on a platter while they are still warm and crunchy. Put out small bowls of ketchup and mustard for dipping. These are best eaten fresh, so serve them as soon as you can.