In a medium saucepan, melt the butter over medium heat. Continue cooking, stirring frequently, until the butter turns golden brown and has a nutty aroma, about 5-7 minutes. Remove from heat and let it cool slightly.
In a large mixing bowl, combine the brown sugar and granulated sugar. Pour the brown butter over the sugars and mix until well combined.
Add the eggs and vanilla extract to the butter-sugar mixture, and mix until smooth.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chocolate chips until evenly distributed.
Cover the dough with plastic wrap and refrigerate for at least 30 minutes to 1 hour. This helps the flavors meld and improves the texture.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes or until the edges are golden brown but the centers are still soft.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.