While the shortbread is cooling, heat brown sugar and butter, whisking constantly, in a heavy medium saucepan over medium until butter is melted and sugar is dissolved, about 3 minutes. Whisk in cream and salt. Bring to a boil and cook, whisking constantly, until butterscotch is thick enough to coat a spoon (bubbling will become less frequent), about 5 minutes. Remove from heat, add tahini and vanilla and whisk until incorporated and smooth.
Pour butterscotch over shortbread and tilt pan to distribute evenly. Chill until set, 30–40 minutes.
Melt chocolate in a microwave-safe bowl in the microwave in 40-second increments, stirring between bursts. (Alternatively, place chocolate in a heatproof bowl set over a saucepan of gently simmering water; bowl should not touch water. Heat, stirring often, until melted and smooth.) Pour over butterscotch and spread evenly to edges of pan; sprinkle with sesame seeds. Chill until chocolate is firm, 1–2 hours.
Using parchment paper overhang, pull bars out of pan and set on a cutting board; remove parchment. Using a serrated knife, slice into 25–36 pieces (5–6 cuts in each direction). Bring to room temperature before serving.