Line 2 cookie sheets with parchment paper or leave the sheets ungreased.
Using electric mixer on medium speed, cream butter, sugar and vanilla in medium mixing bowl until light and fluffy, about 1 1/2 minutes. Stop the mixer once or twice to scrape down bowl with rubber spatula.
Add flour and salt and blend on medium speed about 1 minute. Scrape the bowl and add the nuts with several more turns of the mixer.
Measure out slightly rounded tbls. of dough and shape them into little logs 2 1/2" long. Place the logs 1 1/2" apart on prpared cookie sheets. Flatten slightly with your palm so they are about 1 1/2" wide.
Bake cookies until lightly golden, about 30-35 minutes. Cool on cookie sheets.
When cookies are cool, melt the chocolate in top of double boiler placed over simmering water.
Pour the melted chocolate into a small deep bowl and dip half of each cookie into the chocolate, using the rim of the bowl to scrape any excess chocolate off the bottom of the cookie.
As they are dipped, place the cookies on a large sheet of waxed paper and allow to set until the chocolate hardens, several hours. If it is a humid day, refrigerate them in order to speed the procees. Enjoy!