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1
Stir together amaretti crumbs, cheeses, and 1/2 teaspoon pepper in a small bowl.
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2
Peel sweet potatoes and thinly slice crosswise (1/16 inch thick) with slicer, then generously brush bottom of skillet with some melted butter and cover with one third of sweet-potato slices, overlapping slightly. Dab potatoes with butter, then sprinkle evenly with half of amaretti mixture.
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3
Core and peel apples, then thinly slice crosswise (into 1/16-inch-thick rings) with slicer. Working quickly to prevent apples from discoloring, add half of apples to skillet, overlapping slices slightly, and sprinkle with 1/8 teaspoon salt and 1/8 teaspoon pepper. Top with half of remaining sweet-potato slices and dab with butter, then sprinkle with remaining amaretti mixture. Cover with remaining apples in an even layer. Sprinkle with 1/8 teaspoon salt and 1/8 teaspoon pepper and cover with remaining sweet potatoes. Sprinkle with remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Brush a sheet of foil with butter, then brush galette with any remaining butter and place foil, buttered side down, on top. Place a 10-inch heavy skillet on top of foil to weight galette.
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4
Put oven rack in middle position and preheat oven to 375u00b0F.
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5
Cook potato galette on top of stove over moderate heat until underside is golden, about 10 minutes. Remove top skillet and foil.
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6
Wearing oven mitts, carefully slide galette onto a baking sheet and invert skillet over it. Holding them together, invert galette, browned side up, back into skillet. Cook, uncovered, over moderately high heat until underside is pale golden, about 10 minutes. Transfer skillet to oven and bake galette until a knife inserted in center cuts through easily, about 20 minutes. Slide onto a serving plate.
