In a small sauce over medium heat, add cubed 1/2 cup butter and bring to a boil. Continue heating over medium heat, constantly stirring until the butter has turned a nutty brown color. It may be hard to see the color if your butter is foaming a lot, so periodically take it off the heat to check the color. Remove from heat, place into a heat proof glass and then into the freezer to cool off for 45 minutes to 1 hour, stirring every 15 minutes to promote even cooling. When ready, the butter should be similar in consistency to room temperature butter.
In a medium to large sized bowl, add in flour, baking soda, and salt. Whisk well to combine, then set aside.
In a stand mixer, fitted with the paddle attachment, add room temperature 1/2 cup butter and cooled browned butter. Beat on medium-high until well combined. Add in both sugars and beat for 3 minutes, it should look light and fluffy, and expanded in size.
Add the eggs, yolk and vanilla until smooth, then beat for another 1 minute, scraping at the edges periodically. Add in the dry mixture and mix on low until combined, scraping at the edges. Ensure it is well combined, but do not overmix. Add in the chocolate chips, and fold with a spatula until well dispersed.
Preheat oven to 350°F. Meanwhile, prepare a baking sheet with parchment paper. Using your hands or a scoop, arrange cookies to be about 2 tbsp each. Place all the cookies onto the baking sheet (do not worry about arrangement yet), sprinkle with sea salt if using, and place into the freezer for 30 minutes to rest and cool(don’t skip, see above!)
Remove baking sheet from the freezer, and arrange cookies evenly onto 3 baking sheets fitted with parchment paper (I do 8-9 per sheet). Place into the oven and bake for 9-11 minutes.
Note: If baking in batches, keep cookies cold before baking by keeping them in the fridge.