SOFTEN butter by letting it stand at room temperature or beat with an electric mixer until creamy. Gradually add sugar, beating until light and fluffy, about 4 minutes. Use a rubber spatula to scrape sides of bowl.
ADD egg and vanilla. Beat until mixture is very light and fluffy, about 5 minutes. (The mixure may have a curdled appearance.)
BLEND in flour and salt gradually on low speed. Cover dough with plastic wrap; chill 30 minutes or until firm.
SHAPE chilled dough into log by working it with hands and rolling on counter until it measures 12 inches in length. Roll in chopped pecans to coat. Wrap in plastic wrap; chill at least two hours, or up to three days.
HEAT oven to 350°F. Cut dough into 1/4-inch slices using sharp, thin knife or dental floss (unwaxed). If dough becomes soft during slicing, place in freezer until firm enough to slice neatly.
PLACE cookie slices on ungreased cookie sheet or parchment paper-lined cookie sheet 1 1/2-inches apart.
BAKE 12 to 15 minutes or until cookies are lightly browned. (If cookies are larger, more time may be needed.) Remove cookies from cookie sheet to wire rack to cool.
Bake cookies on parchment paper for easy clean up.