01 - Melt unsalted butter in a light-colored saucepan over medium heat. Continue cooking, stirring frequently, until the butter foams and the milk solids turn golden brown with a fragrant nutty aroma, approximately 4 to 5 minutes. Immediately transfer to a large mixing bowl and allow to cool for 10 minutes.
02 - Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
03 - Whisk the packed brown sugar and granulated sugar into the cooled brown butter until well incorporated. Add the eggs and vanilla extract, beating vigorously until the mixture is smooth and slightly glossy.
04 - In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry mixture to the wet ingredients, folding gently with a spatula until just combined. Avoid overmixing to keep the cookies tender.
05 - Gently fold the semisweet chocolate chips into the dough using a spatula, distributing them evenly throughout.
06 - Scoop heaping tablespoons of dough onto the prepared baking sheets, spacing each portion approximately 2 inches apart to allow for spreading during baking.
07 - Bake one sheet at a time for 10 to 12 minutes, rotating halfway through, until the edges are golden brown and set while the centers remain soft and slightly underbaked.
08 - Remove from the oven and immediately sprinkle with flaky sea salt if desired. Let the cookies rest on the baking sheets for 5 minutes to set, then transfer to a wire rack to cool completely.