In a medium mixing bowl, combine cornmeal, flour, sugar, baking powder, salt, and pepper. In a large mixing bowl, whisk together the eggs and milk. Add the cornmeal mixture to the milk and whisk until just combined. Set aside for 10 minutes.
Add 1 quart of vegetable oil to a large pot or a deep-sided skillet and place over medium-high heat. Line a baking sheet with paper towels and set aside.
Cut the hot dogs into 1-inch pieces. Pour the cornstarch into a zip-top food storage bag and add the hot dog pieces. Seal the bag and shake to coat. As you pull hot dog pieces out of the bag, shake off the excess cornstarch (there should only be a light coating left).
Once oil is heated to 375 degrees F, dip 10 hot dog pieces into the corn dog batter until coated. Add them to the pot and cook until golden brown. Remove them from the oil and place them on the prepared baking sheet to drain.
Repeat dipping and frying the remaining hot dog pieces until they're all cooked. (About halfway through cooking, you'll want to add another 2 cups of oil to the pot. Let it come back up to temperature before continuing to cook.)
Serve warm with ketchup, mustard, or your favorite dipping sauce.
Notes
Each hot dog should yield around six 1-inch pieces, for a total of 72 corn dog bites. (Hebrew National hot dogs come in packs of six.) Yield and nutritional information will vary based on the hot dog brand used.
You can keep the corn dog bites in a 200 degree F oven so they stay warm while you cook the rest of the hot dogs.