Lightly toast the walnuts in a low oven and then let cool. Finely grind the walnuts in a food processor.
Cream the soft butter and sugar together. Add the walnuts, flour, and vanilla and mix well.
With a plain piping tip, pipe the cookie dough in drops onto a buttered and floured pan or onto parchment paper.
Bake in preheated 300 degree oven for 20-30 minutes, or until pale brown in color. When cool, sprinkle powdered sugar over the cookies. 5. Store in an airtight container. The cookie dough feezes well.