In a mixing bowl, combine the self-rising flour and Greek yogurt until a shaggy dough forms.
Transfer dough to a floured surface and knead for 60 seconds until a smooth ball is achieved.
Divide dough into two equal portions and roll out to a thickness of 0.25 inches.
Combine melted butter, minced garlic, parsley, and salt in a small container.
Preheat the air fryer to 375°F (190°C).
Place the dough rounds in the air fryer basket and brush the surface liberally with the garlic butter mixture.
Air fry for 5 to 6 minutes until the edges are golden brown and the center is cooked through.
Remove carefully and serve immediately.