Scrub baby potatoes using a potato brush.
In a shallow stockpot, add potatoes. Pour ice-cold water and sprinkle some salt. Bring to a boil. Cook potatoes until fork tender, about 15 to 18 minutes.
Drain boiled potatoes. Pat dry. Set aside.
In a small bowl, combine butter, dried rosemary, and olive oil.
In a separate container, combine garlic powder and smoked sweet paprika.
Line the entire baking tray with parchment paper. Place boiled potatoes with about 2 to 3 inches of space from each piece.
Smash each baby potato.
Gently transfer smashed potatoes onto the Air Fryer tray. Brush both sides with the butter mixture. Season top side with salt, black pepper, and the garlic mixture. Use two Air Fryer trays.
Slowly insert Air Fryer trays into the pre-heated Air Fryer Oven at 370F (188C). Set at 15 minutes.
After 5 minutes, remove the first Air Fryer tray. See tips or notes when closing the door.
Turn each baby potato and lightly brush with the butter mixture. Season with salt, black pepper, and the remaining garlic mixture. Return to the cooking chamber. Do this to the second tray.
Once the potatoes are crisp tender, remove the first tray. Sprinkle each baby potato with Parmesan cheese on top. Return to the cooking chamber for 1 to 2 minutes or until cheese has melted. Do the same for the second tray.
Garnish with fresh rosemary leaves before serving.