BUTTER AND SUGARS: Using an electric mixer or a stand mixer (fitted with the paddle attachment), beat together the butter, white sugar, and brown sugar until light and fluffy, about 3 to 5 minutes (don't rush this!). Scrape the sides of the bowl as needed.
DRY INGREDIENTS: Beat in the vanilla extract, almond extract, salt, and cornstarch just to combine. Add in the flour and again beat to just combine. Don't over-mix.
SHAPE DOUGH: Divide the dough in two equal pieces. Form each half into a round log shape that is 9 to 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 of chilling.
BAKE: Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or a Silpat liner. Pour the cane sugar onto a large flat plate and set aside. Remove one log at a time and remove the plastic wrap. Brush the outside of the dough with the beaten egg. Immediately roll the dough log into the cane sugar on the plate.
BAKE CONT.: 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 over-baked cookies.
COOL: Remove from the oven, let cookies stand on sheet pan for 2-3 minutes, and then use a metal spatula to transfer cookies to a cooling rack. Allow to cool completely.
CHOCOLATE DRIZZLE: Add chocolate to a bowl and microwave (at 50% power) in bursts of 20 seconds, stirring in between each bursts until the chocolate is melted and smooth. Transfer the chocolate to a plastic bag and snip off the tip with scissors. Drizzle completely cooled shortbread cookies with chocolate and allow the chocolate to harden at room temperature.
STORAGE: Baked cookies are best when used within 2-3 days; store at room temperature in an airtight container.