Toast the sesame seeds in a large skillet over medium-low heat, stirring constantly, until golden, 7 to 10 minutes. Transfer to a bowl and let cool completely.
Beat the butter and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Add the egg, vanilla, salt and baking powder and beat until combined, scraping down the bowl as needed. Reduce the mixer speed to low; add the flour and 1/4 cup of the toasted sesame seeds and beat until just combined. Cover with plastic wrap and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven and preheat to 325 degrees F. Line 2 baking sheets with parchment paper or aluminum foil and butter the parchment or foil. Form teaspoonfuls of dough into small balls, then roll in the remaining 1/2 cup toasted sesame seeds, pressing to coat. Arrange the balls about 2 inches apart on the prepared baking sheets. Bake, switching the position of the pans halfway through, until dark golden around the edges, 15 to 20 minutes. Let cool 1 minute on the baking sheets, then carefully remove the cookies with a thin metal spatula and transfer to racks to cool completely.