Place baby potatoes in a large pot and cover with cold salted water. Bring to a boil and cook for 12-15 minutes until fork-tender. Drain well and let cool slightly.

Preheat the air fryer to 400°F (200°C) for 3-5 minutes.

Place boiled potatoes on a cutting board and use the bottom of a glass or potato masher to gently press down and flatten each potato to about 1/2 inch thickness. Brush with 2 tablespoons olive oil and season with salt, pepper, and paprika.

Place smashed potatoes in a single layer in the air fryer basket. Cook at 400°F for 10 minutes until bottoms are golden and crispy.

While potatoes cook, mix melted butter with minced garlic and remaining 1 tablespoon olive oil.

Carefully flip the potatoes, brush with garlic butter mixture, and air fry for another 8-10 minutes until crispy and golden on both sides.

Remove from air fryer, sprinkle with fresh parsley and Parmesan cheese if using. Serve immediately while hot and crispy.