Preheat oven to 300 degrees F (150 degrees C). Toast sesame seeds on pan, stirring occasionally, until lightly golden (about 10 minutes). Set aside. Increase oven temperature to 350 degrees F (175 degrees C). Grease cookie sheets.
In large mixing bowl, combine flour, baking powder, salt, brown sugar and white sugar. Melt butter over low heat and add to mixture. Separate two of the eggs and add egg yolks. Add the other two eggs and mix well. Mix in toasted sesame oil (optional) and vanilla. Stir until well blended. Add 1 1/2 cups of sesame seeds and mix with electric mixer at medium speed for 10 minutes. Let dough sit for 10 minutes.
Place remaining sesame seeds in shallow pan. Drop level tablespoonful sized pieces of dough into pan. Gently roll in sesame seeds while forming 2-inch long log shape. Taper the ends and place on cookie sheet about 1-inch apart.
Bake until golden, 11 to 13 minutes. Let cool on wire racks.