Preheat the oven to 375 degrees F, and line two baking sheets with parchment paper. Set aside.
In a medium-sized mixing bowl, combine the brown butter with the sugars, vanilla and salt. Once it's completely smooth, add the eggs and stir to combine thoroughly.
Add the baking soda and flour, and mix just until everything is incorporated evenly and there are no signs of dry flour left.
Fold in the chocolate chips.
Dollop or scoop the dough, about 1-½ tablespoons each, onto prepared baking sheets. Leave a couple inches between the, as they will spread when the bake.
Bake the cookies for about 10 minutes. They should be soft when they are removed from the oven, and will firm a bit as they cool.
Let them rest on the baking sheets for at least 10 minutes and then move them to a cooling rack or a large plate.