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Preheat oven to 375°F.
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Melt butter in a large nonstick skillet and remove from heat. Stir in cinnamon, salt, and 1 tablespoon brown sugar, then stir in bread crumbs. Sprinkle one third of crumbs over bottom of a 1-quart shallow baking dish.
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Peel and coarsely chop 2 apples. Cook with water and remaining 2 tablespoons brown sugar in a 1 1/2-quart saucepan, covered, over moderate heat, stirring occasionally, 10 minutes. Purée chopped apples with cooking liquid in a blender.
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Peel remaining 2 apples and cut into 1/4-inch-thick wedges. Arrange wedges over crumbs, then pour hot purée over wedges. Sprinkle with remaining crumbs.
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Bake in middle of oven until top is golden brown and apples are tender, about 40 minutes. Cool on rack 10 minutes and serve with frozen yogurt.