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In a medium bowl, mix together butter, cocoa powder, and vanilla.
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Add 1 cup confectioner’s sugar to cocoa mixture; mix until just incorporated. Add 1 cup confectioner’s sugar; mix until just incorporated. Add remaining 1/2 cup confectioner’s sugar; beat well (mixture will be extremely thick).
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Beat in milk, 1 tablespoon at a time, until desired consistency is reached.
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Spread chocolate frosting on cooled cookies and top with sprinkles.