Preheat oven to 400° F. Line a baking sheet with parchment paper or a silicon silpat. You will either need to prepare two sheets to cook all of the cookies at once, or prepare one sheet and make two batches.
Using a 3 quart saucepan, you will make the brown butter. To do this, add all of the butter to the pan and heat over medium heat. The butter will melt and then bubble and foam. Stir the butter frequently to prevent burning. Continue to stir until brown specs begin to appear and a wonderful nutty aroma forms. It can go from golden brown to burnt rather quickly, so take care not to leave unattended and remove from heat as soon as it is done. Set aside and allow to cool. You will be adding the remaining ingredients to this butter, and if it is too warm it will melt the chocolate chips.
Meanwhile, whisk together flour, baking soda, and salt in a small bowl and set aside.
Once the browned butter has cooled, stir in the brown and granulated sugars. The mixture will resemble wet sand. Next mix in the egg, egg yolks, and vanilla extract.
Add the dry ingredients and stir to combine. Mixture will be rather thick and dry so a wooden spoon works best. Finally, stir in the chocolate chunks. Because of the browned butter, they will not want to stick to the batter.
To form cookies, use a cookie scoop or a regular spoon to form balls that are about 2 tablespoons in size. Roll them into a ball shape and then slightly flatten into a fat disk. If there are loose chocolate chips in the pan, grab a few and press them into the top of the cookie. Set the dough about 2 inches apart on prepared baking sheet.
Bake in preheated oven just until edges of cookies start to brown, about 9 minutes. For best results, you can rotate the baking sheet half way through for even cooking results. Except for the edges, the cookies will look pretty under done when you removed them from the oven.
Remove cookies from oven and allow them to stay on the hot pan for about 5 minutes prior to transferring them to cooling racks with a spatula. As soon as you take them out of the oven, sprinkle with flaked salt (if using).
Serve warm or cool. Once cooled, store in airtight container, or freeze for longer storage.