Cut butter into 1/4 cup sugar and salt with a pastry blender; add vanilla and pecans, stirring well. Stir in flour. Mix well. (Dough will be crumbly.)
Shape into oblong fingers 2 1/2- x 1/2-inch. Bake at 350° for 15 minutes; remove from oven, and immediately roll each cookie in powdered sugar. Cool completely on wire racks.