In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, or the bowl of a standing mixer, cream (beat together) the butter and sugar until light and fluffy. Mix in tahini, vanilla, and sesame oil.
Add the dry ingredients to the butter mixture, and mix to combine.
Shape dough into a flat disk, and wrap in plastic wrap. Refrigerate dough for 1-2 hours.
Preheat oven to 350 degrees F.
Place sesame seeds in a shallow bowl. Cut dough into small squares, and roll the squares into walnut sized balls. Roll the ball of dough in sesame seeds, place it on a silpat lined cookie sheet, and flatten it with your hand.
Bake at 350 degrees F for 10-12 minutes, the edges will be golden brown. Remove cookies from oven, and place the cookie sheet on cooling rack for a few minutes. Cookies will continue to bake and harden a bit. Remove cookies from cookie sheet, and allow to finish cooling directly on the cooling rack.