Preheat your oven to 350°F (175°C). Spread the sesame seeds on a baking sheet and toast them in the oven for about 5-7 minutes, or until they are golden and fragrant. Remove from the oven and let them cool.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the toasted sesame seeds.
Drop spoonfuls of the dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart. Flatten each dough mound slightly with the back of a spoon.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown. The centers may still be soft.
Allow the wafers to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Enjoy your meal!