Using a hand mixer or a stand mixer (fitted with the paddle attachment), beat together the butter, granulated sugar, and brown sugar until light and fluffy, about 3–5 minutes (don’t rush this!). Scrape the sides of the bowl as needed.
Beat in vanilla extract, almond extract, salt, and cornstarch just to combine. Add flour and again beat to just combine. Don’t overmix.
Divide the dough in 2 equal pieces. Form each piece into a round log shape that is 9–9.5 inches long and about 2 inches in diameter. Roll it on the counter to help smooth 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. May be stored this way for up to a week.
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. Removing one log at a time, pull the dough out of the freezer and remove the plastic wrap. Brush the outside of the dough with the beaten egg. Immediately roll the dough log in the sparkling sugar.
Slice each log into 1/2-inch-thick cookies. Place cookies on the prepared tray. Bake cookies until edges are *just* beginning to lightly brown, about 8–11 minutes. Watch carefully to avoid overbaked cookies.
Remove from oven and let cookies stand on sheet pan for 2–3 minutes, then use a metal spatula to transfer cookies 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 until the chocolate is melted and smooth. Transfer the chocolate to a resealable plastic bag and snip off the tip. Drizzle completely cooled cookies with chocolate and allow the chocolate to harden at room temperature.
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Notes
Inspired by Alison Roman's shortbread cookies!Storage: Baked cookies are best enjoyed within 2–3 days; store at room temperature in an airtight container.