Place pieces of butter in a light-colored pan over medium heat. Stir the butter the entire time to keep it moving using a silicone spatula. Once melted, the butter will begin to foam and sizzle around the edges. Keep stirring. In about 5-8 minutes from when you started, the butter will turn golden brown. Some foam will subside and the milk solids at the bottom of the pan will become a toasty brown. It will smell intensely buttery and nutty. Immediately remove the pan from heat and pour the butter into heat-proof bowl to stop the cooking process and let it cool slightly until its just warm to the touch.
To a large mixing bowl, add slightly cooled brown butter, water, and both sugars. Mix by hand or with a hand mixer until combined.
Next, add in the egg and vanilla extract, beat until for about 3-5 minutes until fluffy. You should see the dough become a slightly lighter brown color.
Add in kosher salt, baking soda, and all-purpose flour. Fold into the dough with a wooden spoon or silicone spatula until just combined. It's okay if there are a few streaks of flour.
Add in chocolate chunks and use a silicone spatula to mix the dough until chocolate is evenly distributed into the batter.
Cover with plastic wrap and store in the fridge for at least 1 hour, or overnight - 24 hours. Note: I recommend if you are going to refrigerate these overnight to scoop the dough after an hour, place on a tray lined with parchment paper, wrap and then restore in the fridge. The dough does firm up and this will save you some time and sore arms later. I used a scoop that holds about 3 tablespoons.
Pre-heat an oven to 350 degrees Fahrenheit. Scoop cookie dough (if you haven't already, a cookie scoop that holds about 3 tablespoons) place on a baking sheet roughly 2-3 inches spread out. (Optional: top each dough ball with a chocolate chunk) Once oven is pre-heated bake for 11-13 minutes. Let the cookies cool on the baking pan for 10 minutes.
Enjoy now for lots of gooey chocolate or carefully move cookies to a cooling rack to cool to room temperature.