To a large mixing bowl, add the solidified brown butter, dark brown sugar, and white sugar. Stir until completely combined, using an electric mixer or a wooden spoon (and a bit of arm strength!).
Mix in the eggs, vanilla extract, and milk until well combined.
In another bowl or container, whisk together the flour, baking soda, and salt.
Slowly add the dry ingredients to the wet ingredients, ⅓ of the bowl at a time, folding gently until just combined. Be sure to scrape the edges and the bottom of your mixing bowl.
Finally, pour in the chopped chocolate and distribute.
Cover and chill the dough for 1.5 hours.
Preheat your oven to 350°F. Line a baking sheet with parchment paper.
Use a cookie scoop/spoon to measure out your dough and place it on the parchment-lined pan. Use your hands to form dough balls. Leave space between each one to allow for spreading.
Bake for 9-10 minutes, until they are just golden brown (the middle may still be a little underbaked; that's ok.)
Remove the pan, and bang it on the stove for those bakery-style ripples on top.
Let the cookies rest for 5 minutes; they will finish cooking during this time. Enjoy!