Place the butter in a small sauce pan over medium-high heat and cook for about 2 minutes - stirring almost constantly - until the butter has completely melted and lightly browned. Remove from heat and scrape butter (and any brown specks) into a heatproof bowl. Place the bowl in the refrigerator and bring the butter back to room temperature; this will take about an hour to an hour and a half.
Once the butter is at room temperature...
Preheat oven to 375 degrees (F). Line 2 large baking sheets with parchment paper and set aside.
In a medium sized bowl whisk together the flour, baking soda, and sea salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, add the chilled brown butter and both sugars; beat on medium speed for about 2 minutes, or until light and fluffy. Add in the vanilla and beat smooth. Add the eggs, one at a time, beating well after each addition. Turn the mixer off.
Gently fold in the flour mixture with a wooden spoon, stirring only until the flour begins to disappear. Fold in chocolate chips.
Roll 3 tablespoon sized balls of dough between your palms to form a ball (they should be big; almost a 1/4 cup), then place on prepared sheet (make sure to leave enough room in between each cookie for inevitable spreading). Continue this process until all the dough has been rolled. Place baking sheets in preheated oven - one at a time - and bake for 10 to 11 minutes, or until golden at the edges but still soft in the middle. Let cookies cool for 10 minutes on the sheet before transferring to a wire wrack to cool completely.