Rinse potatoes. Place in a pot, cover with cold salted water, and bring to a boil. Simmer until just fork-tender, 10 to 12 minutes. Drain well and let steam-dry 2 minutes.
Preheat the air fryer to 400°F for 5 minutes.
Transfer potatoes to a sheet of parchment or a cutting board. Use the bottom of a glass to gently press each potato to about 0.5-inch thick.
In a large bowl, toss smashed potatoes with olive oil, garlic powder, paprika, salt, and pepper until evenly coated.
Arrange in a single layer in the air fryer basket. Air fry at 400°F for 12 to 15 minutes, flipping halfway, until crispy and deeply golden.
Sprinkle with Parmesan during the last 2 minutes, if using. Garnish with parsley and serve hot.
Notes
For extra-crispy edges, let drained potatoes steam-dry before smashing. Swap paprika for ranch seasoning or chili powder to change the flavor. Leftovers reheat well in the air fryer at 350°F for 3 to 4 minutes.