In a large bowl of a stand mixer (or using a hand mixer), combine butter, sugar and vanilla until light and fluffy, about 2 minutes.
Add flour and walnuts. Stir until well blended.
Cover dough and chill in the refrigerator for 2 hours. Preheat oven to 375° F degrees. Line a cookie sheet with parchment paper.
Measure about 1 tablespoon of dough and shape it around one chocolate kiss.
Wrap the kiss with the dough.
Roll it to make a ball (cover chocolate completely).
Place dough balls 2 inches apart on prepared baking sheet. Bake at 375° F for 12 minutes or until cookies are set but not browned (the edges may be golden).
Allow cookies to cool on the baking sheet for 5 minutes. While the cookies are still warm, roll them in confectioners' sugar. Set on a wire rack.