For the mozzarella bites: Cut the mozzarella sticks into fourths, creating bite-sized pieces. Set aside.
Add the flour to a shallow dish. Combine the eggs and milk in a second shallow dish. Combine the panko, Parmesan and parsley in a third shallow dish.
Bread the mozzarella by first rolling each piece in the flour, then dunking it in the egg/milk mixture, then placing it in the panko mixture. Use your hands to ensure the entire piece is coated in the breadcrumbs. Transfer to a sheet pan and repeat with the remaining mozzarella pieces. Transfer to the freezer to firm up, about 30 minutes.
Meanwhile, add two inches of oil to a skillet. Heat to 375 degrees F.
For the buffalo sauce: Combine the hot sauce, butter, Worcestershire sauce and apple cider vinegar in a small saucepan over medium heat. Heat until the butter has melted and the sauce is hot, then remove from the heat and cover to keep warm.
Fry the mozzarella bites in batches until golden, between 45 seconds to 1 minute, being careful not to overcook. Carefully remove to drain on a paper towel and immediately sprinkle with a pinch of salt. Serve hot alongside a bowl of warm buffalo sauce, a bowl of ranch dressing and the carrot and celery sticks.