Preheat oven to 325 FLine cookie sheet with Silpat or parchment paper.

In a medium bowl, whisk together the flour and baking soda.  Set aside.

Cut butter into chunks (so that the butter melts more evenly) and place in a thick-bottomed pan over medium heat. Whisk butter frequently. Once melted, the butter will foam up a bit, then subside. The butter's color will move from a lemony-yellow to a darker golden, then to a bronze-tan.  Watch carefully as lightly browned specks begin to form at the bottom of the pan. Smell the butter; it should have a nutty aroma. Once it's been sufficiently browned to your taste, remove from heat and transfer to a cool bowl to help stop the butter from cooking further and burning.  Some people strain out the brown bits, but for this recipe, you want them.

Add brown sugar and vanilla to a mixing bowl.  Pour in the cooled brown butter and combine on low speed until blended well.  Add flour/soda mixture and blend.

With your hands, roll dough into a long strip, about the thickness of the diameter of a quarter. (I’ve found that larger cookies tend to have a different texture.) Cut into 1/2″ thick rounds, flatten slightly, pressing with your hand. Sprinkle tops with a bit of pulverized sea salt.

Bake for 12 minutes in center of oven or until lightly golden. Don’t overbake or the cookies will be too dry and crumbly. (I found the right timing in my oven by baking a few test cookies at different times. Ovens can vary in temperature.)