Heat 1 inch of oil in a deep pan to 330 degrees F.
Place the flour in a shallow dish, season with salt and pepper then stir. Beat together the egg with salt and pepper in a second shallow dish. Place the finely crushed garlic and herb pita chips in a third shallow dish. Dip each cheese stick half in flour, shaking off the excess, then in the egg, then repeat the flour and egg. Lastly, dip each in the pita chips, pressing to coat. At this point, freeze for 15 minutes to firm the sticks before frying.
Combine the marinara, cream and pesto in a small sauce pot. Stir and heat through.
Fry the mozzarella sticks in the hot oil, turning, until golden brown on all sides, about 30 seconds. Remove to a paper towel-lined plate. Serve immediately with the dipping sauce.