Add the butter to a medium pot or skillet, preferably one that is light in color (so you can see the color of the butter). Turn the heat to medium.
Cook, stirring every 1-2 minutes with a wooden spoon. After a couple minutes, the butter will start to foam. Keep watching it. Eventually the butter will turn brown and you will see tiny brown specks. The smell will turn nutty. You might not be able to see the color under the foam very well, which is part of the reason you need to stir. Once it is brown and it looks silty at the bottom, it is done.
Immediately pour the browned butter into a large bowl or stand mixer. Add the white sugar and brown sugar and beat well.
With the beaters on, add the eggs. (If you don't have enough hands for this, then wait a few minutes to let the butter mixture cool so you don't curdle your eggs. Or you could beat the eggs in a separate bowl and then add them all at once.)
Add the vanilla and stir.
Add half the flour, but don't stir. Use a small spoon to stir the baking soda and salt into the flour, then beat the flour into the dough.
Add the remaining flour and stir, but stop when the dough is still dry and you can still see flour.
Add all the chocolate chips. Stir together just until the flour is incorporated. Do not over beat.
At this point you need to chill the dough. You can cover the bowl and throw it in the fridge for 1-2 hours. (or up to 24 hours!) Or you can shape the dough as described below and freeze for 30 minutes (or refrigerate for 30-45 minutes.) Shape the dough and place it right on the pan if you have room in your freezer, otherwise put them in ziplocks to freeze them.***
Preheat your oven to 350 degrees F. Line baking sheets with silpats or parchment paper.
To shape the dough, use a 1/4 measuring cup. Form the dough into an egg shape (as opposed to a sphere). Place the dough on the prepared cookie sheets, with at least 2 inches between each cookie.
Bake at 350 for about 11-14 minutes. Your bake time will depend on your method and length of chilling, so keep an eye on them so they don't get overdone.
Take the cookies out when they are just barely starting to turn golden on top, and the centers are not shiny (or, if you like really soft cookies, a little shine is okay.)
Immediately after taking them out of the oven, use your fingers to push several chocolate chips into the tops of each cookie.
Let them set up on the pan for 5 minutes, then remove to a cooling rack.
Eat these cookies with milk!!