Melt the butter in a skillet over medium-low heat. Lower the heat to low and skim the foam off the top. I keep a bowl of water on the side to dip the spoon in. Pour the clarified butter into a container. If you don't use all of the butter for the potatoes, reserve it for other recipes that call for butter.
Preheat the oven to 450˚F. Slice the potatoes on a mandolin. If you don't have one, slice 1/8" thick, being careful to slice the slices in an even thickness. I use a small mandolin that rests on the counter, and it works great. Peel and core the apple, and slice the same way.
Place a clean 6 inch, oven-proof skillet on a stove top over medium-high heat for 30 seconds, flip the pan over on the stove to directly heat the inside of the pan for 15 seconds. Return the pan, right side up, on the stove over the heat. Lower the heat to low, and 2 tsp of melted clarified butter to the pan. Add the first layer of potatoes, overlapping the slices by about 40% over each other. Spread on one-quarter of the apple slices and 1 Tbsp raisins. Lightly salt and pepper, and add a pinch of the herbs. Carefully brush generously with butter.
Add another layer of potatoes, one-quarter of the apples, raisins, and salt the pepper. Sprinkle on a little brown sugar. I used about 1/2 tsp, but feel free to adjust for your amount of sweetness. Generously brush with butter.
Repeat for at least 2 more layers, depending on the height of the sides of the pan. I ended up with a total of 5 layers, alternating the brown sugar and herbs every other layer. Press down on the layers to add the final layer. Finish with a layer of potatoes, salt and pepper, and a generous brushing of butter.
Slide the pan into the preheated oven and bake for 25 minutes, or until the top is crispy along the edges, and the potatoes are tender. Remove from the heat, wait a couple minutes, place a plate over the top of the skillet, and a towel around the handle. Flip the plate and pan so that the pan rests on the counter, and the potatoes are now upside down. Gently tap the skillet on the plate a couple of times, and carefully remove the skillet. If some potatoes are stuck to the bottom, gingerly remove with a small offset spatula, and arrange on the top of the dish.
Finish with a flurry of herbs and serve warm. Be sure to have a sharp knife handy to slice the Sweet Potatoes Anna into pie-shaped slices.