Chop up peanut butter cups and refrigerate. In a large bowl, cream butter and sugars. Mix in peanut butter, egg, and vanilla.
Next, add the flour and baking soda and mix well, being careful to not over mix. Add the quick oats, chocolate chips, chocolate chunks, and peanut butter cups.
Scoop out dough onto a baking sheet, and flatten slightly with the back of a spoon. Refrigerate the dough for at least an hour.
Preheat oven to 350 degrees F. Bake cookies for 8 to 10 minutes.
Once out of the oven, press down again with the back of a spoon to get the crinkly top effect. Let cool before enjoying. Store in an airtight container.