Line baking sheets with parchment paper. I suggest using light colored baking sheets.

In a medium mixing bowl, using a stand mixer or hand mixer, cream together butter, sugar, sugar, and vanilla extract for 3-4 minutes, or until light and fluffy. Scrape down the sides of the bowl, halfway through to ensure even mixing.

Add the flour and mix just until combined. Fold in the chocolate chunks. Mix just until everything is combined. You may want to press everything together with your hands.

Divide the dough into two equal portions. Place each portion on a large sheet of plastic wrap. Fold the plastic wrap over the dough so you can shape it without it sticking to your hands. Roll the log back and forth to create an even cylinder. Use your hands to form each piece into a log about 2 to 2¼ inches in diameter. Repeat with the second portion. Wrap the logs tightly in plastic wrap. Refrigerate both logs until they are very firm, about 2 hours.

Preheat your oven to 350 degrees. Remove the shortbread dough logs from the refrigerator and let them come to room temperature for about 10-15 minutes.

In a small bowl, beat the egg and brush it over the chilled logs. Pour some demerara, turbinado sugar, or sparkling sugar on a plate or into a shallow dish, then roll each dough log in the sugar until the outside is evenly coated.

Using a sharp knife, slice each log into ½-inch thick rounds. Arrange the rounds on the prepared baking sheets, leaving about 1 inch of space between them. Since they are shortbread cookies, they will not spread too much.

Bake for 11 to 14 minutes, or until the edges are just beginning to turn golden. Remove from the oven and sprinkle with sea salt flakes. Let the cookies cool slightly before serving.