Brown your butter: Add butter to a saucepan and place over medium heat. The butter will begin to crackle, and start to foam. Whisk constantly during at this point. After a couple of minutes, the butter will begin turn a golden amber color on the bottom of the saucepan. Continue to whisk and remove from heat as soon as the butter begins to brown. Immediately transfer the butter to a bowl to prevent burning. Set aside to cool for 10 minutes or until cool enough to touch. With a whisk, electric mixer, or stand mixer with paddle attachment, mix the brown butter and sugars until well combined for about 1 minute. Then beat in the eggs and vanilla until combined.
In a separate large bowl, whisk together the flour, baking soda, and salt. Slowly add the dry ingredients to the wet ingredients and beat on low-speed just until combined. Add both chocolate chips and mix on low speed until just incorporated into the dough.
Measure 3 heaping tablespoons of the dough or use a large cookie scoop. Place dough balls on cookie sheet, give them a little space in between.
Place formed dough balls in the refrigerator to chill for at least 1 hour, or up to 12-24 hours. Do not try to speed up this process. The dough needs to chill in order to be perfect.
Preheat your oven to 350 degrees F and line a baking sheet with parchment paper.Once chilled, bake the cookies 12-15 minutes or until the edges of the cookies begin to turn golden brown. They will look a bit underdone in the middle, but they continue to cook once out of the oven. Don't over bake! Cool the cookies on the sheets for 5 minutes to allow them to set up, then sprinkle each cookie with sea salt. Remove the cooled cookies from the baking sheets and transfer to a wire rack to cool completely. Makes 15 large cookies.