Prep. Scrub the potatoes and dry them completely. Slice a thin sliver off the flattest side of each potato so it sits flat without rolling.
Slice. Place a chopstick or wooden spoon handle along each side of a potato. Cut straight down at ¼-inch intervals along the length of the potato, letting the chopsticks stop your knife about ½ inch from the bottom. Repeat with the remaining potatoes.
Soak (optional). Place the sliced potatoes in cold water for 10–15 minutes to rinse out excess starch, then pat them completely dry inside and out.
Preheat. Preheat the air fryer to 375°F.
Season. Brush the potatoes with olive oil, working a little between the slices, and season with the salt and pepper.
First cook. Arrange the potatoes cut side up in a single layer in the air fryer basket, leaving space between them. Air fry at 375°F for 20 minutes.
Make the garlic butter. Stir together the melted butter, minced garlic, parsley, thyme, and rosemary.
Butter and finish. Gently press the slices apart with a fork, brush the garlic herb butter generously over the potatoes and down into the cuts, and air fry another 10–15 minutes, until a knife slides into the center of the thickest potato with no resistance and the edges are golden and crisp.
Serve. Brush with any remaining butter, top with flaky salt and fresh parsley, and serve immediately.