In the bowl of a stand mixer, add butter and confectioners' sugar. Beat on medium until creamy.
Add vanilla, and mix until incorprated.
In a separate bowl add flour, cornstarch, and salt.
With the mixer on low, add in flour mixture, one cup at a time.
Gently fold in ¾ cup toffee bits (reserving ¼ cup for topping).
Add dough to a lightly floured work surface and roll into a 6-inch log, about 3 inches in diameter. Wrap in plastic and seal the ends. Place the dough in the refrigerator to chill for 1 hour, or until firm.
When ready, preheat the oven to 350°F and line 2 large baking sheets with parchment paper.
Remove the dough from the refrigerator and place it on a cutting board.
Slice into ¼-inch cookies and place cookies onto each prepared baking sheet about 1 inch apart. Top with reserved toffee bits.
Bake 10-12 minutes, or until lightly browned.
Let the cookies rest for 5 minutes before transferring them to a wire rack to cool.