In a food processor or mini chopper, add in the cup of quick cooking oats. Process until the oats have formed a flour. I didn't sift mine since I didn't mind if the bigger pieces of oats were in my cookies. Feel free to sift the flour to make sure you get all the bits of oats that didn't get processed well enough.
In a large mixing bowl, add butter, shortening, and peanut butter. Mix on medium until creamed. Scrape down the sides.
Add in the brown sugar and mix on medium until light and fluffy.
Add in the vanilla and egg. Mix on medium until the egg is well incorporated. Scrape down the sides.
Add in the oatmeal flour, all-purpose flour, baking soda, and baking powder. Mix on low until the flour is almost completely incorporated. Turn the mixer on medium and continue beating until the cookie dough comes together.
Refrigerate for at least 1 hour. Just before the hour is up, preheat the oven to 350 degrees.
Using a cookie scoop, scoop the cookies onto a baking sheet, Parchment paper isn't necessary, but feel free to use it. I would only place 6 cookies on the baking sheet so they have room to spread. Place 5-6 Reese's Pieces on the tops of the cookies. Press them in slightly.
Place in the oven for about 10 minutes or until the edges start to brown. Let them sit for about 10 minutes before moving them to a cooling rack.