Preheat oven to 325 degrees F. Adjust oven rack to the middle position. Line a baking sheet with parchment paper or a silpad.
In a medium-size bowl, combine the flour, baking powder, and salt; set aside.
With an electric mixer at medium-high speed, beat the butter and brown sugar together until fluffy, approximately 2 minutes. Reduce the speed to medium and beat in the egg and vanilla extract until combined. Add the flour mixture and beat until incorporated. Fold in the cooled toasted sesame seeds.
Drop heaping teaspoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart (this is important as the cookies will spread).
Bake until the tops of the cookies bubble and the edges turn deep brown, approximately 8 to 9 minutes.
Remove from oven and let the cookies cool on the baking sheet for 2 minutes. As these are paper-thin cookies, this allows the cookies to finish baking from the residual heat of the baking sheet, as well as letting them set up enough so that they don't fall apart when transferred. Then transfer to a wire rack to cool completely, about 15 minutes.
The cookies may be stored in an airtight container.
* Toasting Sesame Seeds - Heat the sesame seeds in a dry pan over medium-low heat, or on a baking sheet in a 275 degree F. oven, until golden and fragrant, approximately 3 to 4 minutes. Watch carefully so the seeds do not burn.
Benne Wafers Cookie Recipe: https://whatscookingamerica.net/cookie/bennewafers.htm