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Combine the flour, powdered sugar, and cocoa powder; set aside.
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Cream the butter and vanilla with an electric mixer on medium-low speed until fluffy.
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Gradually stir in the flour mixture until well blended.
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Cover and chill dough for at least 30 minutes.
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Preheat oven to 350°F.
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Shape dough into 1" balls; shape balls into 2" logs about 1/2" thick.
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Space 2" apart on ungreased cookie sheets.
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Bake for 12 minutes, or until set.
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Cool on cookie sheets for 2 minutes; transfer cookies to wire racks and cool completely.
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Melt the white chocolate chips in a saucepan over very low heat, stirring, until smooth.
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Place the sprinkles in a small bowl.
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Dip each end of the cooled cookies into the white chocolate, then the sprinkles.
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Return to the wire racks and let stand until the chocolate has set, about 25 minutes.