Heat the butter in a 10-inch skillet over medium-high heat until melted, about 2 minutes. Continue cooking, swirling pan constantly until butter is dark golden brown and has a nutty aroma, 1 to 3 minutes. Remove skillet from heat and, using a heatproof spatula, transfer browned butter to the bowl of a stand mixer; set aside to cool to room temperature, about 45-60 minutes.
Meanwhile, whisk together the flour, baking soda, and salt in a medium bowl; set aside.
When the butter has cooled, add the sugars and beat on medium speed until combined, about 2 minutes. Add the vanilla extract, eggs, and yolk and beat until combined. With the mixer on low, gradually add the flour mixture and mix until combined. Scrape down the sides of the bowl and mix briefly. Add the chocolate chips and stir with a rubber spatula to combine.
Using a 2-ounce ice cream scoop, form balls of dough and place them on a parchment lined cookie sheet. Cover the sheet with plastic wrap and refrigerate for at least 24 hours and up to 72 hours. (Once firm, cookies can be placed in a freezer safe plastic bag.)
Preheat the oven to 325º F. Place the cookie dough balls about 2-inches apart on a separate parchment lined baking sheet. Bake until lightly golden, about 20-22 minutes. Remove from the oven and transfer the cookies still on the sheet to a wire rack (the centers will continue to set up on the hot baking sheet) and cool for 5 minutes. Serve warm or transfer the cookies to the wire rack to cool completely. Enjoy with a tall glass of milk!