Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil.

Cut a pocket into each chicken breast. Evenly stuff pocket of each chicken breast with 1 slice mozzarella cheese and 1 tablespoon pesto.

Beat together eggs and remaining 1 tablespoon pesto in a bowl. Place Parmesan cheese in a shallow dish. Dip chicken in egg mixture and then coat with Parmesan cheese. Place coated chicken breast onto the prepared baking sheet.

Bake in the preheated oven until chicken is no longer pink in the center and juices are running clear, 20 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).