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Set oven rack in the center; preheat to 400°F .
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Lightly oil 3 baking sheets or coat with nonstick cooking spray, and dust them with flour, shaking off excess.
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Combine oats, corn syrup and oil in a medium bowl.
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Melt butter in a small saucepan over low heat and cook until it begins to turn a light, nutty brown, 1 1/2 to 2 minutes. (Be careful not to burn the butter.)
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Pour into the oat mixture and stir to combine. Set aside.
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Beat egg and sugar in a mixing bowl with an electric mixer until thickened and pale, about 5 minutes. Blend in vanilla.
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Stir together flour, baking powder and salt in a small bowl; fold into the egg mixture.
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Add the oat mixture and dried cherries; stir gently to combine.
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Spoon the batter by teaspoonfuls, about 2 inches apart, onto the prepared baking sheets.
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Bake, one sheet at a time, for about 4 minutes, or until the cookies are golden and lacy.
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Let cool on the baking sheet for 2 minutes, then carefully remove cookies from the baking sheet and cool on a flat surface (not a rack).