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MELT butter in a large skillet over medium-high heat; add garlic, and saute 1 to 2 minutes.
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Add half-and-half and chicken broth.
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Bring to a boil, and cook 8 minutes or until reduced by half.
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WHISK together lemon juice and cornstarch until smooth.
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Whisk lemon juice and 1/2 teaspoon pepper into butter mixture, and cook, whisking constantly, 2 minutes or until thickened.
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Remove from heat.
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DO NOT ADD BASIL UNTIL READY TO SERVE.