3 apples, cored, peeled, and cut into 1-inch chunks
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Cook sugar and water in a medium nonstick pot over medium-high heat, until sugar caramelizes, about 4 minutes. Reduce heat to low, and stir in apples; then cook, covered, until apples soften, about 6 minutes. Slightly mash apples up with a fork so th
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for the cake
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1 cup (2 sticks) unsalted butter, at room temperature