Use a mandolin to slice the potatoes as thinly as you can.
Brush the bottom of a heatproof 7 x 2 inch pan with butter. Arrange one slice of potato in the middle. Now create concentric, overlapping circles of potato, making sure you go all the way to the edges of the pan since the potatoes will shrink as they cook.
Place this pan with its single layer of potatoes on the stove top and start heating it on medium. You are doing this to get the bottom layer well browned.
Continue to place layer upon layer of potatoes, continuing in concentric circles, brushing with lots of butter between layers. Press down on the layers so that the bottom will brown well.
Once you are done with the last layer, sprinkle any remaining salt and pepper and pour any remaining butter all over the potatoes.
Cover the pan with foil. Place the pan in the air fryer basket and set the air fryer to to 400°F for 30 minutes. Then remove the foil, and cook at 400°F for another 10 minutes.
Using a spatula, loosen the edges of the potatoes and upturn them on to a serving plate.
Do not rinse the potato slices. You need the starch between the layers for the potatoes to stick together.
Do not skimp on the butter. There are only four ingredients in this dish. You NEED that butter. Cut calories somewhere else.
Do not skip the step where I ask you to brown the pan with potatoes on the stovetop first. Listen. You know me. #ruthlessefficiency. If I tell you to follow an additional step, you can bet there's a reason why. In this case, the reason is simply that you need a good, firm brown crust on the bottom potatoes. The beauty of Potatoes Anna is the combination of a slightly crispy crust, along with the creamy potatoes inside. You can't get that crust with just the air fryer. Trust me. I tried it.
Take my advice and start with that center slice of potato as you begin layering. It really serves as an anchor point that will make the concentric circles in your Pomme Anna that much more even and symmetrical. You just don't get the same symmetry when you start placing potatoes from the sides first.