Place pecans in food processor. Process using on/off pulsing action until pecans are ground, but not pasty.
Beat butter and 1/2 cup powdered sugar in large bowl with electric mixer at medium speed until light and fluffy, scraping down side of bowl once. Gradually add 1 cup flour, vanilla and salt. Beat at low speed until well blended, scraping down side of bowl once. Stir in remaining 1 cup flour and ground nuts with spoon. Form dough into a ball; wrap in plastic wrap and refrigerate 1 hour or until firm.
Preheat oven to 350. Roll tablespoons of dough into 1-inch balls. Place 1 inch apart on ungreased cookie sheets. Bake 12 to 15 minutes or until pale golden brown. Let cookies stand on cookie sheets 2 minutes.
Meanwhile, place 1/2 cup powdered sugar in 13x9-inch glass dish. Transfer hot cookies to powdered sugar. Roll cookies in remaining sugar, coating well. Let cookies cool in sugar.
Sift more sugar over sugar-coated cookies before serving. Store tightly covered at room temperature or freeze up to 1 month. Makes about 4 dozen cookies.