Trim skewers so they fit into air fryer basket, if needed. Soak in water at least 30 minutes to prevent burning.
Meanwhile, in a large bowl, toss chicken, oil, Italian seasoning, 2 teaspoons salt, and 1 teaspoon garlic powder until coated.
Thread chicken onto skewers (about 6 pieces per skewer). Working in batches if needed, arrange skewers in air fryer basket in a single layer, spacing about ½" apart.
Air fry at 400° for 8 minutes.
Meanwhile, in a small bowl, mix butter, parsley, Parmesan, and remaining 1 teaspoon garlic powder and ½ teaspoon salt.
Flip skewers, generously brush with garlic-herb butter, and continue to air fry until browned, cooked though, and an instant-read thermometer inserted into thickest part of chicken registers 165°, about 4 minutes more.
Generously brush skewers with garlic-herb butter and arrange on a platter. Serve with remaining garlic-herb butter alongside.
