Line two baking sheets with silpat mats or parchment paper. Using a stand mixer fitted with the paddle attachment or an electric hand mixer, beat the butter, sugars, and vanilla on medium-high till it’s super light and fluffy (3 to 5 minutes for a stand mixer; 6 to 8 for a hand mixer). Do not skimp on this, be patient, the difference a few minutes in the mixer can make are amazing (see picture). Using a spatula, scrape down the sides of the bowl every minute or so.
Add flour and chopped chocolate chunks slowly (chopping the chocolate makes it easer to cut later), and mix it until the flour is just incorporated, you do not want to over mix the dough. If necessary, knead the dough with your hands to make sure the flour is totally incorporated.
Divide the dough in half, placing each half on a large piece of plastic wrap. Fold the plastic over so that it covers the dough to protect your hands from getting all sticky. Using your hands, form the dough into a log shape; rolling it on the counter will help you smooth it out, but don’t worry about getting it totally perfect. (Don't be afraid to make them compact. Shortbread is supposed to be dense. That's part of why it's so good. The original instructions say to make the logs 6 inches long, and 2 to 2¼-inches in diameter. I’ve found they are easier to cut later if they logs are little thinner and longer, so I like to make them 1 ½ inches in diameter. Chill until totally firm, about 2 hours.
Heat the oven to 350 degrees Fahrenheit. Using a large knife slice the log in to ½ inch slices and roll the edges of the cookie in brown sugar. If the slices fall apart when cutting, just push the dough back together.
Place them on the prepared baking sheets about 1 inch apart (they won’t spread much). Sprinkle with sea salt if you like. Bake until the edges are just beginning to brown, 12 to 15 minutes. Let cool before eating.