Make herb butter: Mix softened butter with garlic, parsley, lemon zest, salt, and pepper. Shape into a log on plastic wrap, roll tight, and refrigerate for at least 30 minutes until firm.
Pound chicken: Place each breast between plastic wrap and pound to ½-inch even thickness. Season lightly with salt and pepper.
Stuff and roll: Slice the butter log into 4 portions. Place one in the center of each breast. Fold in the sides, then roll up tightly from the bottom like a burrito. Secure the seam with 2–3 toothpicks. Freeze rolled chicken for 15 minutes.
Set up breading: Place flour, beaten eggs, and seasoned panko in three separate shallow dishes.
Bread: Coat each roll in flour (shake off excess), dip in egg, press firmly into panko on all sides. For extra crunch, repeat egg and panko dip.
Preheat air fryer to 375°F (190°C) for 5 minutes. Spray basket with cooking spray.
Air fry: Place kievs seam-side down. Spray tops generously. Cook at 375°F for 10 minutes, spray again, then cook 10–15 more minutes until golden and internal temp reads 165°F (74°C).
Rest: Remove toothpicks. Rest for 5 minutes before serving. Serve over mashed potatoes so the herb butter acts as a sauce.