In a large bowl, cream butter, sugar and vanilla until light and fluffy, 5-7 minutes. Gradually add flour and mix well. Fold in walnuts. Refrigerate dough until firm, 2-3 hours.
Preheat oven to 375°. Shape into 1-in. balls. Flatten balls and place a chocolate kiss in the center of each; pinch dough together around kiss. Place 2 in. apart on ungreased baking sheets.
Bake until set but not browned, 12 minutes. Cool 1 minute; remove from pans to wire racks.
Sift together 2/3 cup confectioners' sugar and cocoa. While cookies are still warm, roll half in cocoa mixture and half in remaining confectioners' sugar. Cool completely. Store in an airtight container.
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