Preheat the oven to 400°. Coarsely grate 4 of the potatoes into a colander. Toss with 1 tablespoon of kosher salt and let drain for 5 minutes. Using your hands, squeeze out as much liquid as possible from the potatoes and transfer to a bowl. Grate the apple and add to the potatoes. Add the onion, 1 tablespoon of the olive oil and the sage and toss well. Season with pepper.
Using a sharp knife or a mandoline, slice the remaining potato 1/4 inch thick. In a 10-inch nonstick ovenproof skillet, heat 1 tablespoon of the olive oil. Arrange the potato slices in the skillet in concentric circles. Season with salt and pepper and cook over moderate heat, pressing down on the potatoes with a spatula a few times, until the slices brown around the edges, about 5 minutes.
Spoon the grated potato mixture into the skillet, pressing firmly to make a neat cake. Transfer the skillet to the oven and bake for about 35 minutes, or until browned and crisp on the bottom. Invert the cake onto a flat plate. Add the remaining 1/2 tablespoon of olive oil to the skillet. Slide the potato cake back into the skillet and cook over moderately low heat until nicely browned on the bottom, about 5 minutes. Slide the cake onto a cutting board and garnish with the chives. Cut into 4 wedges and serve on plates with the Horseradish Cream.
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