In your stand mixer, mix the brown sugar and eggs together until well mixed.
Mix in the vanilla, then add the peanut butter and mix until it is well incorporated.
Freeze the dough for 15 minutes before baking. (This is a recommended step to help the cookies retain their shape better, but it's not required.)
Use a scoop or spoon to form the dough into 12 2" balls and place them on the parchment lined baking sheet. You can also use a smaller spoon/scoop to make smaller cookies (that's what I did and made 36 cookies).
Sprinkle the dough balls with a bit of the course sea salt just before baking.
For the 2" balls, bake for 20-22 minutes. For smaller balls bake 16-18 minutes. The cookies are done baking when they are lightly golden and cracked on top.
Cook completely before serving.
Recipe by My Man's Belly at http://mymansbelly.com/2016/07/08/flourless-salty-sweet-peanut-butter-cookies/