Preheat oven to 325°. Line a rimmed baking sheet with parchment paper.
Spread sesame seeds in a single layer on prepared pan. Toast until lightly browned, 5 to 7 minutes. Let cool.
Line rimmed baking sheets with parchment paper.
In a large bowl, beat butter and brown sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg, beating well. Beat in zest and vanilla.
In a small bowl, whisk together flour, salt, and baking powder. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined. Beat in toasted sesame seeds. Using a 2-teaspoon scoop, drop batter 3 inches apart onto prepared pans. (Cookies will spread.)
Bake until deep golden brown, about 15 minutes. Let cool on pans for 1 minute. Remove from pans, and let cool completely on wire racks. Store in an airtight container with layers separated by wax paper.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/benne-wafers/