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In small bowl, cream butter and sugar until light and fluffy.
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Beat in lemon juice.
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Combine flour, cornstarch and lemon peel; gradually add to creamed mixture and mix well.
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Shape into 1 1/2 inch roll; wrap in plastic wrap.
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Refrigerate for 1 hour or until firm.
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Unwrap and cut into 1/4 inch slices.
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Place 2 inches apart on ungreased baking sheets.
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Bake at 350 for 8-10 minutes or until edges are golden brown.
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Cool completely on pans on wire racks.
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Frosting:.
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In small bowl beat butter until fluffy.
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Add confectioners' sugar, lemon juice and peel.
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beat until smooth.
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Spread over cooled cookes; sprinkle with additional lemon peel if desired.
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Let stand until set. Store in an airtight container.