Preheat oven to 350 °F. Grease 4 cookie sheets with vegetable shortening.
In medium bowl of electric mixer with paddle attached, beat butter with sugar on medium speed until well blended and fluffy.
Gradually add egg and vanilla, and continue beating until mixture increases in volume.
In another bowl, combine sesame seeds, flour, salt and baking powder.
Add to creamed mixture in four parts, beating after each addition on low speed just until blended.
Drop dough by teaspoonfuls 2 inches apart on prepared cookie sheets.
Bake for 8 minutes or until cookies have spread and are lightly browned.
Remove from oven and let cool for 30 seconds. With spatula, carefully transfer to wire rack to cool.
If cookies become too hard, return to warm oven for about a minute to soften slightly.
Store in an airtight container. Makes about 75 small cookies.