Preheat the oven to 350 degrees. Line two baking sheets with parchment paper or silicone baking mats 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 the ingredients are incorporated.
With a tablespoon-size cookie scoop or spoon, form 1-tablespoon dough balls and place them on the prepared cookie sheets. Bake for 10 minutes, or until the edges are slightly browned (it's okay if they crack). Remove from the oven, sprinkle a little sea salt over the cookies, and pat down slightly with the back of a flat spatula. Allow to cool for 10 minutes before transferring to a wire cooling rack.