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In 2-quart saucepan, thoroughly combine sugar and flour.
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With wire whisk, gradually stir in milk until smooth.
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Cook over medium-high heat, stirring frequently, until mixture has thickened and boils.
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Reduce heat to low; cook 2 minutes, stirring constantly.
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Remove from heat and cool completely.
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In medium bowl, with mixer at medium speed, beat butter until light and fluffy.
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Gradually beat in milk mixture; beat in vanilla.