Step 1
Whisk ¾ cup (83 g) powdered sugar, ½ cup (1 stick) unsalted butter, room temperature, ⅓ cup well-stirred tahini, room temperature, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and 1½ tsp. vanilla extract in a medium bowl until sugar is dissolved and mixture is smooth. Mix in 1½ cups (188 g) all-purpose flour with a rubber spatula until no pockets of dry flour remain. Set tahini dough aside.
Step 2
Whisk remaining ¾ cup (83 g) powdered sugar, ½ cup (1 stick) unsalted butter, room temperature, ⅓ cup well-stirred tahini, room temperature, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and 1½ tsp. vanilla extract in another medium bowl until sugar is dissolved and mixture is smooth. Mix in ½ cup (45 g) Dutch-process cocoa powder and remaining 1 cup (125 g) all-purpose flour with spatula until no pockets of dry flour or cocoa powder remain.
Step 3
Roll chocolate dough into about a 7½x2½” log; tightly wrap in plastic, twisting ends to help shape log. Repeat with reserved tahini dough (try to make logs the same thickness.) Chill logs on a flat surface, turning and rolling every 30 minutes, to keep round, at least 2 hours and up to 1 day.
Step 4
Let dough sit at room temperature 15 minutes. Unwrap and, using a long, thin knife, cut each log in half lengthwise. Lay each half cut side down; cut each in half lengthwise to create 4 pieces total. (If logs are brittle and crack when cut, let sit to warm 5 minutes longer.) Brush cut sides of dough with water, then press together 2 tahini pieces and 2 chocolate pieces, alternating the colors, to re-form into a log. Repeat with remaining 4 pieces of dough to make a second log. Wrap each log in plastic and gently roll on counter several times to re-form and help cut sides adhere to one another. Twist ends of plastic to help shape. Chill logs at least 2 hours and up to 1 day.
Step 5
Place racks in upper and lower thirds of oven and preheat to 325°. Unwrap logs; let sit at room temperature 15 minutes.
Step 6
Brush logs lightly with water. Place ½ cup raw white and/or black sesame seeds on a rimmed baking sheet or in a 13×9″ baking dish and roll logs in seeds, gently pressing into sides to adhere, until evenly coated. Save any leftover seeds for another use. Trim ends off of each log, then cut logs into ½”-thick slices, rotating after each cut to help logs keep their shape and pressing gently together if they start breaking apart. (If logs are brittle and crack when cut, let sit to warm 5 minutes longer.) Divide between 2 parchment-lined baking sheets, spacing at least 2″ apart. Freeze 10 minutes.
Step 7
Bake cookies, rotating baking sheets top to bottom and front to back halfway through, until golden brown, 24–26 minutes. Let cool on baking sheets. (Cookies might be a bit soft when they come out of the oven, but they will firm up as they cool.)
Do Ahead: Cookies can be baked 4 days ahead. Store airtight at room temperature.