Start by drying the chicken breasts with paper towels; they should feel nice and dry to the touch. This helps the breading stick later on. If they are still wet, the breadcrumbs will not adhere properly, resulting in soggy breading.
In a bowl, whisk the egg lightly until it is frothy and bubbly. Add in the garlic salt, oregano, and a dash of black pepper, ensuring to blend thoroughly to avoid seasoning clumps.
Grab a chicken breast and slice it open like a pocket but do not cut all the way through. Stuff it generously with the burrata and a couple of slices of prosciutto, making sure it feels snug without overstuffing.
Dip each stuffed chicken breast into the egg mixture, then coat it in breadcrumbs. Ensure each piece is fully covered for that lovely, crispy crust. If some breading falls off, pick it up and reapply it.
Preheat your air fryer to get it nice and hot before cooking. You want to hear a slight hiss when you add the chicken. If it is not preheated, the chicken will not achieve that desired crispiness.
Carefully place the stuffed chicken breasts in the air fryer basket and drizzle them with olive oil. Ensure they are not crowded to achieve that golden brown crust.
After about 20 minutes, use a meat thermometer to check if each chicken breast has reached the proper temperature. They should feel firm and look golden brown, avoiding cutting them open immediately to prevent the filling from oozing out.
Once cooked, allow the chicken to rest for a few minutes before slicing. This gives the juices time to redistribute for a juicy result.