Heat the oven to 375°F and lightly oil a baking dish or ovenproof skillet. Pat the chicken breasts dry with paper towels so the seasoning adheres and the chicken browns properly.

Using a sharp knife, cut a horizontal pocket into the thickest part of each chicken breast, taking care not to cut all the way through. Season the inside and outside with Italian seasoning, the divided kosher salt, black pepper, and minced garlic.

Pat the tomato slices dry, then fill each chicken pocket with mozzarella, tomato, and basil. Avoid overfilling, and secure the openings with toothpicks if needed.

Heat the olive oil in an oven-safe skillet over medium-high heat. Sear the stuffed chicken for about 2–3 minutes per side, until lightly browned; this step may be skipped if preferred.

Transfer the skillet to the oven and bake for approximately 20–25 minutes, or until the thickest part of each breast reaches 165°F on an instant-read thermometer. If using a baking dish, transfer the seared chicken carefully before baking.

Let the chicken rest for 5 minutes after baking, then remove the toothpicks. Drizzle with 1–2 tablespoons of balsamic glaze immediately before serving.