Beat butter and peanut butter in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, baking powder, and baking soda; beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in flour and cocoa powder. Stir in rolled oats with a wooden spoon. Stir in candy pieces.
Drop cookie dough from a 1/4-cup measure, 3 inches apart, onto an ungreased cookie sheet. Bake in a 375 degrees F oven for 10 minutes. Press 5 to 7 candy eyeballs into the cookies and bake 5 to 7 minutes more or until edges are firm. Transfer to wire racks and cool. Store in an airtight container or plastic bag at room temperature up to 3 days.