Whisk the flour, baking powder and salt together in a medium bowl. Set aside.
Beat the butter and sugars in a large bowl using an electric mixer until well combined, about 3 minutes. Add the tahini, vanilla and egg and beat until light, about 3 minutes. Stir in the flour. Form the dough into two 12-inch logs that are 1 1/2 to 2 inches in diameter, wrap in plastic wrap and refrigerate until very firm, 4 hours and up to overnight.
Preheat the oven to 325 degrees F. Line two or three baking sheets with parchment paper.
Remove one log of dough from the refrigerator and slice into 1/4- inch-thick slices. Place the sesame seeds on a plate. Coat the cookies in sesame seeds by pressing them lightly into the seeds, and place them on the prepared baking sheets. Bake until lightly golden around the edges, about 12 minutes, rotating the baking sheets top to bottom and front to back halfway through cooking. Cool the cookies on the baking sheet for 10 minutes, and then transfer to a rack to cool completely. Repeat with the remaining log.