In a bowl attached to a stand mixer (or with a hand mixer), cream together butter, oil, sugars, and peanut butter until light and fluffy. Mix in eggs and vanilla.
With mixer on low, gradually add in dry ingredients: flour, baking soda, salt. Mix in oatmeal.
With medium-sized cookie scoop, scoop out dough on cookie sheet about 2″ apart. Bake for 10 minutes or until tops are set. Let cool on sheets for 10 minutes then transfer onto wire rack to cool completely. Store in airtight container.