Beat 3/4 cup butter at medium speed with an electric mixer until creamy; gradually add sugar. Add egg and vanilla, mixing well.
Combine flour and salt; add to butter mixture, mixing until blended. Stir in 1 cup chocolate morsels.
Shape dough into 1 1/2- x 1/2-inch logs. Place on ungreased cookie sheets.
Bake at 350F for 12 to 15 minutes or until set. Remove to wire racks to cool.
Combine remaining 1 cup chocolate morsels and remaining 1/4 cup butter in a small heavy saucepan; cook over low heat, stirring often, until chocolate melts. Dip ends of cookies into mixture, and roll in chopped walnuts. Place on wax paper until chocolate is firm. Store in an airtight container; freeze up to 6 months, if desired.