Beat butter with both sugars until pale and fluffy, 2–3 minutes.
Mix in vanilla and fine salt until smooth.
Whisk flour, cornstarch, and baking powder in a separate bowl.
Add dry ingredients to the butter mixture in two additions; mix just until a soft dough forms.
Fold in toffee bits until evenly distributed.
Divide dough in half; shape each into a 1¾-inch-thick log.
Wrap logs tightly and chill until very firm, 1–2 hours.
Heat oven to 350°F. Line two baking sheets with parchment.
Slice chilled logs into ¼-inch rounds and set 2 inches apart on sheets.
Bake 10–12 minutes, until edges turn light golden. Rotate pans halfway through.
Cool 5 minutes on the sheet, then transfer to a rack. Sprinkle flaky salt if using.