Preheat your air fryer at 350 degrees F, air fryer setting, for about 4-5 minutes.
Spray a baking or pizza pan with non-stick cooking spray. Mix the shredded mozzarella, cheese, grated Parmesan cheese, egg, and seasonings in a large mixing bowl.
Place the prepared dough into the pan and air fry at 350 degrees F, air fryer setting, for 2-3 minutes, remove as soon as it turns a golden brown. Using a pair of tongs, flip the bread, and air fry the other side for another 2 to 4 minutes, until the bread is golden brown.
Sprinkle with some extra mozzarella or Parmesan cheese, then air fry for about 2 to 3 minutes at 350 degrees F, air fryer setting, until the cheese is melted.
Let the bread cool slightly before slicing.