Prep the potatoes: Rinse and dry the mini potatoes thoroughly. Dry skins help them crisp up better.
Slice the Hasselback cuts: Place two chopsticks or wooden skewers on either side of a potato. Slice crosswise every 1/8 inch, stopping when the knife hits the sticks so you don’t cut all the way through.
Repeat with all potatoes.
Make the seasoning mixture: In a small bowl, combine olive oil, melted butter, garlic, salt, pepper, rosemary, and smoked paprika if using. Stir well.
Coat the potatoes: Toss the potatoes with the mixture, gently prying open a few slices so some of the seasoning seeps inside. A pastry brush helps work the mixture into the cuts.
Preheat the air fryer: Set to 375°F (190°C) for 3 minutes.
Lightly spray the basket if sticking is a concern.
Air fry, round one: Arrange potatoes cut-side up in a single layer. Cook for 12 minutes.
Baste and continue: Open the basket, brush or spoon any leftover butter-oil mixture over the potatoes, and gently fan the slices with tongs if they’re sticking together. Cook another 8–12 minutes, until edges are deeply golden and centers are tender when pierced.
Optional finish: Sprinkle with grated Parmesan in the last 2 minutes for a savory crust.
Garnish and serve: Transfer to a plate, shower with fresh parsley, and taste for salt.
Serve hot.