In a bowl, beat the butter, peanut butter, brown sugar, and granulated sugar together until well-combined and fluffy.
Add in eggs and vanilla. Beat until completely mixed.
Add in flour, oats, baking soda, and salt. Beat just until mixed and a sticky dough forms.
Scoop golf-ball-sized scoops of dough onto parchment lined baking sheets, placing 8 cookies to a sheet as far apart as possible (these cookies SPREAD).
Bake at 350 degrees for 12 to 15 minutes, until cookies are browned around the edges and tops look mostly set.
Allow cookies to cool on baking sheet for 2 minutes and then remove to a cooling rack to allow to cool completely. Makes 2 dozen cookies.