Pat chicken breasts dry with paper towels. On a clean cutting board, hold your hand flat on top of the chicken breast. Using a sharp knife, cut a horizontal pocket along the thicker side of the breast, being careful not to cut all the way through. The pocket should extend about ¾ across the width of the breast.
In a small bowl, combine ½ teaspoon salt, black pepper, and Italian seasoning. Rub 1 tablespoon olive oil over chicken breasts, then sprinkle with the seasoning mixture, ensuring to season both the outside and inside of the pocket.
In a medium bowl, combine diced tomatoes, minced garlic, chopped basil (reserving some for garnish), mozzarella, remaining salt, and 1 tablespoon olive oil. Gently mix to combine.
Carefully stuff each chicken pocket with the caprese mixture, dividing evenly between breasts. Secure the opening with toothpicks or kitchen twine to prevent filling from leaking during cooking.
Preheat your air fryer to 375°F for 3 minutes.
Place stuffed chicken breasts in the air fryer basket, ensuring they don't touch for proper air circulation. Cook for 15-18 minutes, turning halfway through the cooking time.
Verify internal temperature reaches 165°F at the thickest part using an instant-read thermometer. The cheese should be fully melted, and juices should run clear.
Remove chicken from the air fryer and let rest for 5 minutes to allow for carryover cooking and juice redistribution. Remove toothpicks or twine, slice on the bias, and drizzle with balsamic glaze before serving. Garnish with reserved fresh basil.