In a medium bowl, whisk together flour, baking powder, and salt.
Add Greek yogurt and stir until a shaggy dough forms.
Turn dough onto a lightly floured surface and knead for 1 to 2 minutes until smooth.
Divide dough into 4 equal portions and roll each into a 0.25-inch thick circle.
Preheat air fryer to 400°F (200°C).
Place dough rounds in the air fryer basket in a single layer, working in batches if necessary.
Cook for 3 minutes, flip, and cook for an additional 2 to 3 minutes until golden brown and puffed.
In a small bowl, combine melted butter, minced garlic, and parsley.
Brush the hot flatbreads with the garlic butter mixture immediately upon removal from the air fryer.