In a stainless steel skillet (or another light-bottomed pan) over medium-high heat, melt butter, swirling the pan occasionally. The butter will begin to foam, which signals the water in the butter is boiling off. (Watch closely at this stage.) Tiny brown specks of milk solids will begin to appear at the bottom of the pan; constantly stir and scrape these off using a spatula so they don't stick.
As soon as the butter turns chestnut brown and smells nutty, remove the pan from the heat. Pour the browned butter into a large heat-safe bowl and set aside to cool to room temperature (about 15-20 minutes).
Preheat the oven to 325°F. Spray a 9x13-inch baking dish with nonstick cooking spray. Set aside.
In a medium bowl, whisk together the flour, salt, and baking soda. Set aside.
To the bowl with the cooled browned butter, add brown sugar and granulated sugar. Whisk until combined.
Add the eggs and vanilla extract. Whisk until well combined.
Add the dry ingredients to the wet mixture. Mix until just combined.
Mix in 2 cups of chocolate chips.
Transfer the dough to the prepared pan. Press evenly into the pan using a spatula or your fingertips. Top with the remaining chocolate chips.
Bake for 30-32 minutes, or until the top is light golden brown and slightly firm to the touch.