Using a hand mixer or stand mixer fitted with a paddle attachment, cream together butter, granulated sugar, brown sugar, vanilla extract, and salt until incorporated.
Sift in the flour. With a spatula, scrape the bowl and mix until the dough starts to come together with a spatula. The dough will look crumbly at first, but it will come together as you continue mixing. Then, add the finely chopped chocolate and mix until well combined.
Press the dough into a log about 2-inch/5cm wide. Wrap the dough with parchment paper or plastic wrap and chill until very firm for at least 2 hours.
Preheat oven to 350F/180°C and line two baking pans with parchment papers.
Slice the log into a 1/3 to 1/2-inch or about 8-12 mm thick with a sharp knife. Arrange the slices on the baking pan, spacing 1-inch apart. If the cookie dough splits or breaks apart during slicing, just piece it back together into a round.
Sprinkle the top of each slice with sea salt flakes, if desired.
Bake for 13-15 minutes or until the bottom edges of the cookies are golden brown in color. Rotate the baking sheets halfway through for even baking.
Transfer to a wire sheet to cool completely.
Notes
Use cake flour for light, crisp, and tender cookies. Use all-purpose flour for softer and chewier cookies.