Preheat your oven to 350°F (175°C).
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the egg and vanilla extract, and mix well.
In another bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the sesame seeds.
Drop spoonfuls of dough onto a baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are golden brown.
Let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.