Preheat the oven to 350°F / 175°C. Line a cookie sheet with parchment paper.
Add the butter to a small saute pan or saucepan. Set the butter over medium heat, stirring occasionally until the butter bubbles up, then turns amber in color (this took me ~2 minutes.)
Pour the brown butter into a small mixing bowl and set it to chill in the freezer for 5 minutes.
Once the butter has chilled, mix in the light brown sugar and granulated sugar, followed by the milk and vanilla.
Add in the flour, baking soda, and salt. Mix together just until a few flour streaks remain, then mix in the chocolate chips just until no flour streaks remain.
Set the cookie dough in the freezer to chill for 5 minutes.
Scoop out all the cookie dough and roll it into one large ball. Top the cookie with extra chocolate chips as desired. Bake for 14-16 minutes, until the edges are golden brown and the middle of the cookie no longer looks “wet.”
Allow the cookie to rest on the hot baking sheet for 5-10 minutes before transferring it to a wire rack to cool (or just before enjoying it warm.) Serve and enjoy!