In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the sugar and vanilla; beat until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour, the sesame seed, and the pecans or almonds. Divide dough in half. If dough is too sticky, wrap each half in parchment, waxed paper or plastic wrap and chill in the refrigerator about 1 hour or until dough is easy to handle.
On a lightly floured surface, roll half of the dough to 1/8-inch thickness. Using 2-inch cookie cutters, cut dough into desired shapes. Place 1 inch apart on an ungreased cookie sheet.
Bake cookies in a 375 degree F. oven for 7 to 8 minutes or until edges are lightly browned. Transfer cookies to a wire rack; cool. Repeat with remaining dough.
In a heavy, small saucepan combine semisweet chocolate and shortening; heat over low heat until melted, stirring occasionally. Drizzle chocolate mixture over cookies. Let cookies stand until chocolate is set. Makes 56 cookies.