In the bowl of an electric mixer add the butter, sugar, and brown sugar, and beat on medium speed for 2-3 minutes until smooth. Add the vanilla, and slowly beat in the eggs one at a time. Blend in the peanut butter.
In a small bowl combine the flour, oats, salt, and baking soda and set aside.
Slowly add the dry ingredients to the wet in three additions and mix until just combined. Add the chocolate chunks. Put the cookie dough in the fridge for a minimum of 1 hour, or up to overnight.
When ready to bake, preheat the oven to 350 degrees. Scoop dough, roll into balls, and place onto a parchment paper lined baking sheet. Bake for 10-12 minutes, do not over bake!! They will continue to cook once they come out. Sprinkle with a little bit of sea salt immediately after you take them out of the oven. Cool on the pan for a few minutes then transfer to a cooling rack.