In a shallow bowl, combine the salt, pepper, onion powder, and garlic powder.
Cut each chicken breast in half lengthwise.
Place each chicken cutlet between two sheets of plastic wrap or parchment paper. Using a meat mallet or rolling pin, flatten the chicken to about 1/2-inch thick.
Season each flattened chicken breast evenly with the half of the seasoning mix, then place 2 slices of ham and 2 slices of cheese on each breast.
Carefully roll up each chicken breast, using the plastic wrap to help keep it tight. Wrap it completely in plastic wrap and refrigerate for 30 minutes to help the rolls hold their shape.
In a shallow bowl, beat the eggs and in another bowl, mix the panko crumbs with the remaining seasoning mix.
Preheat your air fryer to 375 degrees F.
Remove the raw chicken from the plastic wrap and dip each roll first in the egg wash, then coat them evenly with the seasoned panko breadcrumb mixture.
Lightly spray the air fryer basket with cooking spray and place the breaded chicken rolls in a single layer in the basket, seam-side down, leaving some space between each roll.
Cook your chicken for 25-30 minutes, checking halfway through cooking; if the top is golden brown, carefully flip the rolls. If not, continue cooking and check every 5 minutes.
Use an instant-read thermometer to check if the internal temperature of the chicken has reached 165 degrees F, the exterior should be golden brown and crispy.
Let the chicken rest for 2-3 minutes before slicing on a cutting board and serving. This helps the juices redistribute and makes for easier slicing.