a deep-fry thermometer; 6 wooden chopsticks or 8-inch skewers
Fill a large pot halfway with the oil. (You should have a least 4 inches of oil in the pot.) Bring the oil to 350 degrees F over medium to medium-high heat. Line a plate with a paper towel.
Meanwhile, in a large bowl, combine the corn muffin mix, milk, egg, pickled jalapeno juice and a pinch of salt and whisk until blended. If the batter is really thick, add a little more milk. (It should be the consistency of thick pancake batter.) Let rest for about 5 minutes.
Skewer each hot dog on a chopstick or skewer. Place the flour on a plate or sheet tray. Working in batches of three, dredge the hot dogs in the flour so they are completely coated, making sure to shake off any excess flour. Dip the hot dogs in the batter and turn to completely coat. Gently slide them into the oil and fry, rotating occasionally so they evenly brown, until golden brown all over, 4 to 6 minutes. Remove to the lined plate. Serve with mustard for dipping.