Using a hand mixer or stand mixer (fitted with the paddle attachment), beat together butter, granulated sugar, and brown sugar until light and fluffy, about 3 to 5 minutes. Scrape the sides of the bowl as needed.
Beat in vanilla extract, almond extract, salt, and cornstarch just to combine. Add in flour and again beat to just combine. Don’t overmix.
Fold in the chopped toffee and gently knead the dough together. It will seem crumbly at first!
Divide dough in 2 equal halves. Form each half into a log shape that is 9 to 9.5 inches long and about 2 inches in diameter. Roll it on the counter to help smooth it out. (Use plastic wrap to avoid touching the dough with hands and warming the butter too much.) Wrap tightly in plastic wrap and place in the fridge to chill for 2 hours.
Preheat oven to 350°F. Line a sheet pan with parchment paper or a silicone baking mat. Pour the cane sugar onto a large, flat plate and set aside. Remove one log at a time from the fridge and remove plastic wrap. Brush the outside of the dough with the beaten egg. Immediately roll the dough log in the cane sugar on the plate.
Slice each log into 1/2-inch thick cookies. Place cookies on the prepared tray. Bake until edges are just beginning to lightly brown, about 8–11 minutes. Watch carefully to avoid overbaked cookies!
Remove from oven and transfer to a cooling rack. Allow to cool completely.
Add chocolate to a bowl and microwave (at 50% power) in bursts of 20 seconds, stirring between each burst for 15 seconds until chocolate is melted and smooth.
Transfer the chocolate to a resealable plastic bag and cut off a corner. Drizzle completely cooled cookies with chocolate and allow chocolate to harden at room temperature.
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Notes
Inspired by Alison Roman’s shortbread cookies!Storage: Cookies are best when eaten within 2–3 days; store at room temperature in an airtight container.