Lay chicken down on a cutting board. Place your hand on top of the chicken and carefully slice each breast in half. Place 1 breast as a time in a large resealable bag, remove the air, and seal. Use a meat mallet to pound the chicken until it's 1/4" thick.
Place a cheese stick at one end of the chicken, as well as 8 slices of pepperoni. Tightly roll the chicken over the cheese and pepperoni. Use a toothpick to keep the chicken and filling in place.
In a wide-mouthed bowl, whisk the egg. In a second wide-mouthed bowl, combine Italian seasoning and parmesan. Dip chicken in the egg, then in the parmesan and place on your prepared baking sheet.