Wash the mini potatoes and cut them in half. If any are larger than the others, cut them into quarters so that all the pieces are roughly the same size for even cooking. Pat them dry thoroughly with a kitchen towel.
In a large bowl, toss the halved potatoes with olive oil, minced garlic, crushed dried rosemary, smoked paprika, salt, and black pepper. Make sure every piece is evenly coated.
Preheat the air fryer to 400 degrees F. Arrange the potatoes in the basket in a single layer, cut side down. This gives you the crispiest flat surface. Avoid overcrowding the basket.
Air fry for 15 to 18 minutes, shaking the basket once around the 10-minute mark, until the potatoes are golden and crispy on the outside and completely tender on the inside when pierced with a fork.
Transfer the potatoes to a serving bowl and immediately toss with the grated parmesan cheese and chopped fresh parsley. The residual heat will slightly melt the parmesan and bring everything together. Serve hot as a side dish.