Pour about 2-3 inches of neutral oil into a deep fryer, Dutch oven, or large pot. Heat to 350°F (175°C) over medium-high heat. Use a clip-on thermometer if possible.
Pat hot dogs dry with paper towels. Insert wooden skewers or popsicle sticks into each hot dog, leaving enough handle to hold comfortably.
In a large bowl, whisk together cornmeal, all-purpose flour, sugar, baking powder, and salt.
In a separate bowl, whisk together sourdough discard, milk, egg, olive oil, and honey until smooth.
Pour wet ingredients into the dry ingredients and whisk gently until just combined. The batter should be thick but pourable, like pancake batter. Transfer the batter to a tall glass for easy dipping, be sure to leave about 1 inch at the top of the glass.
Dip each hot dog straight down into the batter, twirl to coat, and swirl as you pull it up. Let excess batter drip off. When you first place the corn dog into the oil, hold it at an angle for about 5 seconds so the batter can start to set before you let it go. Carefully place 2–3 corn dogs into the hot oil at a time. Fry for 2 - 3 minutes until golden brown, turning as needed.
Use tongs to transfer the corn dogs to a wire rack to cool slightly. Serve warm with your favorite sauces and condiments.