In a large bowl of a stand mixer or using an electric hand mixer, cream together the softened butter, tahini and powdered sugar. Add the vanilla extract and beat until dissolved.
Add the flour, a little at a time, and use a wooden spoon or rubber spatula to mix until well combined. Remove the dough from the bowl and use your hands to tightly pack the dough. Divide the dough in half.
Shape each half portion of dough on a plastic wrap into a log about 1-2 inches wide. Roll each log in sesame seeds, if using, until well coated.
Wrap each log in the plastic wrap, twisting at each end and chill in the fridge for at least one hour or overnight.
Preheat the oven to 350°F and line 2 baking sheets with parchment paper.
Slice the logs into ¼ inch thickness and place on the prepared baking sheets, arranging them so they’re about 2 inches apart.
Bake for 8-10 minutes or until cookies are firm, slightly expanded and the bottoms are lightly golden.
Cool on the baking sheet for 10 minutes, then transfer to wire racks to finish cooling completely.