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In the bowl of an electric mixer, beat room temperature butter until lightly fluffy. Add the sifted powdered sugar 1 spoon at a time and mix well. It will get light in color and bigger in volume.
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Add vanilla and cocoa, and the milk, scraping down the sides of the bowl as you work.
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Turn mixer on medium high. Beat frosting until light, fluffy and of spreading consistency.
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If the frosting is too thick, slowly add more milk or half and half, one tablespoon at a time, until it reaches the desired consistency.
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You can use the frosting immediately, or store it in the refrigerator for 3 days.