Cook butter in a 8-9 inch cast iron skillet over medium heat, whisking constantly while it crackles and foams. Cook until butter browns and turns a golden amber color, about 5-7 minutes. Remove from heat and immediately pour into a large bowl (or your electric mixing bowl) and let cool until cool enough to touch, about 10 minutes.

Combine flour, baking soda, and salt in a medium bowl. Set aside.

Add all sugar to the browned butter. Using an electric mixer or on medium speed or a whisk, beat until fully incorporated. Add egg and vanilla extract and beat until mixture lightens and begins to thicken.

Reduce mixer speed to low. Add the dry ingredients, gradually, and beat until just combined with each addition. Fold or mix in chocolate chips with a wooden spoon or rubber spatula. Refrigerate dough for at least 30 minutes to thicken before baking.

Place a rack in the middle of the oven and preheat to 350°F.

Place the cookie dough in a well-greased 8-9 inch skillet, pressing down firmly until evenly distributed throughout the entire bottom of the skillet. You're looking for roughly 1/2 inch thick cookie dough all around. Note, brown butter cookie dough is stiffer than traditional chocolate chip cookie dough. This is normal.

Bake for 20-25 minutes or until the edges are golden and the center is still a little gooey. The cookie will continue to cook as it cools in the skillet. Don't overbake. Top with ice cream and hot fudge and dig in with spoons after the cookie has slightly cooled. Best eaten warm.