Beat the butter, granulated and brown sugars, and vanilla with a stand mixer, bowl locked, until light and fluffy, scraping down the bowl as needed and mixing until no buttery chunks remain. Add flour, and mix just until combined and all flour is moistened. Add chocolate chunks, mix just until incorporated. Mixture will look crumbly.

Use the same process with a hand mixer, but start with room temperature or softened butter.

Transfer dough to a large sheet of parchment paper and form into a log about 2.25 to 2.5 inches in diameter. Chill until totally firm, about 2 hours.

Heat your oven to 350°F. Line one or two large baking sheets with parchment paper. Lightly beat the egg and open up your chilled cookie logs. Brush the egg over the sides of the logs. Sprinkle the coarse sugar on the parchment or plastic wrap and roll the logs into it, coating them. Using a sharp serrated knife, cut logs into 1/2-inch thick rounds.

Arrange cookie slices on prepared sheets one inch apart and sprinkle each with a few flakes of salt. Bake for 12 to 15 minutes, or until the edges are just beginning to get golden brown. Let cool slightly before transferring the cookies to wire racks to cool completely.