Preheat the air fryer or oven to 375°F (190°C).
Cut a pocket into each chicken breast. Be careful not to cut all the way through.
In a bowl, mix the mozzarella cheese, salami, sun-dried tomatoes, Italian seasoning, salt, and pepper.
Stuff each chicken breast with the mixture. If needed, seal the edges with toothpicks.
Brush the outside of the chicken with olive oil.
Place the stuffed chicken in the air fryer and cook for 20-25 minutes, or bake in the oven for 25-30 minutes. Make sure the chicken is cooked through, and the juices run clear.
Let the chicken rest for a few minutes before serving.