Scrub the russet potatoes and dry them thoroughly.
Slice across each potato at 1/8 to 1/4 inch intervals, stopping about 1/4 inch from the bottom so the potato stays intact. Lay a chopstick or wooden spoon handle along each side of the potato to stop the knife from cutting all the way through.
Brush the potatoes with the melted butter, working it down between the slices. Sprinkle with the garlic powder, kosher salt, and black pepper, again getting the seasoning into the cuts.
Preheat the air fryer to 390°F (200°C). Arrange the potatoes in a single layer in the basket and cook for 30 to 40 minutes, until softened and fanned open. A knife should slide into the thickest part without resistance.
Remove the potatoes and tuck the cheddar slices down into the cuts.
Return to the air fryer for 5 to 10 minutes, until the cheese is melted and bubbling.
Garnish with the chopped chives and parsley. Serve hot, with sour cream if desired.