In a small bowl, mix softened unsalted butter with chopped fresh herbs, kosher salt, and black pepper until well combined.
Pat the turkey breast dry with paper towels to help the skin crisp.
Carefully loosen the skin from the meat by sliding your fingers underneath, working gently to avoid tearing.
Spread about three-quarters of the herb butter evenly under the skin across the breast.
Rub the remaining butter on top of the skin; season lightly with additional salt and pepper if desired.
Preheat the air fryer to 360°F for 3 minutes.
Place the turkey breast skin-side up in the air fryer basket, leaving space for air circulation.
Cook at 360°F for 45 to 50 minutes (start checking at 40 minutes for smaller breasts).
Check the internal temperature at the thickest part; it should read 165°F.
Remove and rest on a cutting board for 10 minutes before slicing so juices redistribute.