Melt the butter over medium heat in a light-colored pan, stirring often, until the solids separate and turn golden brown and you can smell a nutty aroma. Place the brown butter in a large bowl and transfer it to the refrigerator or freezer until it hardens.
Once the butter has hardened, break it into pieces, and add the white and brown sugar to the bowl. Use a hand mixer to cream the butter and the sugars on low speed until incorporated.
Add the vanilla extract and one egg to the bowl. Mix on low speed until incorporated. Scrape down the sides of the bowl and add the second egg. Mix on low speed until combined, scraping down the sides of the bowl as needed.
In a separate bowl, combine the all-purpose flour and baking soda.
Pour half of the flour mixture into the creamed butter mixture and mix on low speed until combined. Scrape down the sides of the bowl, add in the remaining flour, and mix on low speed until a dough forms. Fold in the chocolate chips until evenly combined.
Divide and roll the dough into balls about 2 Tbsp in size. Place the dough balls on a sheet pan lined with parchment paper about two inches apart. Chill the dough in your refrigerator, uncovered, for at least an hour, but preferably overnight.
When ready to bake, preheat the oven to 350°F. Press the chilled cookie dough balls down with two fingers to flatten slightly.
Bake the cookies for 4 minutes, rotate the sheet pan front to back, then bake for an additional 4 minutes, or until the edges are a light golden brown. Let the cookies cool on the sheet pan for at least 5 minutes before transferring to a cooling rack to finish cooling.
*If using unsalted butter, add 1/2 teaspoon of finely ground salt (like fine sea salt) or 1 teaspoon of coarsely ground salt (like kosher salt) to the butter.