Preheat your oven to 375°F (190°C).
In a medium saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter turns golden brown and develops a nutty aroma, about 3-5 minutes. Remove from heat and let it cool slightly.
In a mixing bowl, whisk together the flour, baking soda, and salt.
In a large mixing bowl, combine the brown sugar, granulated sugar, and browned butter. Mix until well combined and smooth.
Beat in the egg, followed by the vanilla extract, until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix.
Gently fold in the chocolate chips until evenly distributed throughout the cookie dough.
Pour the cookie dough into the hot skillet, spreading it out evenly.
Place the skillet back in the oven and bake for 15-20 minutes, or until the edges are golden brown and the center is set.