In a bowl, beat butter and confectioners' sugar until smooth and creamy. Add vanilla.
On low speed, beat in flour and pecans. Wrap dough in plastic wrap and refrigerate 1 to 2 hours, until firm.
Heat oven to 325°. Pinch off pieces of dough in rounded teaspoonfuls. Roll into logs, taper ends and bend into crescents. Place on ungreased baking sheets.
Bake at 325° for 19 to 20 minutes, until lightly browned.
Remove cookies to a wire rack. Sprinkle with a heavy layer of confectioners' sugar. Cool completely. Sprinkle again with confectioners' sugar.