Heat the oven to 350ºF. Place the chocolate in a medium heatproof bowl and place the bowl in the oven, stirring every 30 seconds or so, until the chocolate melts just enough to be stirred smooth, about 3 minutes. Lightly grease a large baking sheet.
Whisk together the flour, baking powder, and salt in a small bowl.
Using an electric mixer on medium speed, beat the butter and brown sugar until light and fluffy, 3 to 4 minutes. Beat in the melted chocolate, tahini, egg, vanilla extract, and almond extract. Mix in the flour mixture on low speed.
Cover and chill the dough for 30 minutes or up to 8 hours (if chilling that long, let the dough warm up for 30 minutes before rolling). Roll into 1-inch balls between your palms and place the balls on the prepared sheet, leaving at least 1-inch between each ball. Dip a fork in cold water and flatten the balls by pressing the fork in a crisscross pattern on each one. Sprinkle with the sesame seeds.
Bake until the cookies are almost firm and the tops are barely dry (slightly underbaked), 6 to 8 minutes. Cool 5 minutes on the sheet, then transfer to racks to cool completely.
Tip: These cookies make terrific gifts; wrap them in parchment paper to protect the decorative packaging from oil stains.