Preheat the oven to 350 degrees. Line two baking sheets with parchment paper and set aside.
In a bowl, whisk together the brown sugar and eggs, then whisk in the vanilla.
With a wooden spoon, stir in the peanut butter until a thick and creamy batter forms; it is ready when no plain peanut butter can be seen and all of the ingredients are incorporated.
With a tablespoon-size cookie scoop or spoon, form the dough balls and place them on the prepared baking sheets. Bake for 12 to 15 minutes*, or until the edges are slightly browned.
Remove from the oven and sprinkle with sea salt and pat down slightly with the back of a flat spatula. Allow to cool for about 10 minutes before transferring to a wire cooling rack.