Place potatoes and water in a covered vented microwave-safe dish. Microwave on HIGH for 7 to 9 minutes, turning halfway through, until a skewer passes through every center easily. Drain and let steam escape for 5 minutes.
Flatten each potato on a plate with the bottom of a glass to about 1/2 inch thick, keeping the rough pieces attached. Brush both faces with olive oil and season with salt and pepper.
Preheat a 6-quart air fryer to 400°F for 3 minutes. Transfer 6 potatoes to the basket in one layer with a thin spatula and cook for 8 minutes.
Turn carefully and cook for 6 to 8 minutes more until crisp at the edges. Transfer to a rack and repeat with remaining potatoes.
Melt butter in a small microwave-safe bowl for 15 to 20 seconds and stir in garlic powder and dill. Brush the finished potatoes lightly with the flavored butter and serve 3 per portion.