Beat the butter, granulated and brown sugars and vanilla with an electric mixer until light and fluffy, scraping down bowl as needed. Add flour and mix just until combined. Add chocolate chunks and mix just until incorporated. (Mixture will look crumbly.)
Divide dough between 2 sheets of parchment paper, waxed paper or plastic wrap and use your hands to form the dough halves into logs about 2 to 2 1/4 inches in diameter. Chill until totally firm, about 2 hours. I hastened this along in the freezer (30 minutes, tops) but did feel that the cookies were better after resting longer. (But do know that it works!)
When you're ready to bake the cookies, heat the oven to 350 degrees F. Line 1 or 2 large baking sheets with parchment paper.
Lightly beat the egg and unwrap the chilled cookie logs to brush it over the sides. Sprinkle the coarse sugar on the open wrapping and roll the logs into it, coating them.
Using a sharp serrated knife, cut logs into 1/2-inch-thick rounds. You're going to hit some chocolate chunks, so saw gently, squeezing the cookie to keep it from breaking if needed. Arrange cookie slices on prepared baking sheets 1 inch apart (they don't spread much) and sprinkle each with a few flakes of sea salt. Bake until the edges are just beginning to get golden brown, 12 to 15 minutes. Let cool slightly before transferring the cookies you don't eat immediately to a wire rack to cool.
The dough can be made ahead and stored, tightly wrapped in plastic, up to 1 week in the fridge, or 1 month in the freezer. Baked cookies keep in an airtight container for 5 days, or so I've heard.