Preheat the oven to 350 F. In a large bowl, mix together cake mix, eggs, and vegetable oil until smooth. Use a cookie scoop to place the cookies onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.
In a large bowl, mix together butter, peanut butter, sugar, and vanilla extract until smooth. Spread frosting onto half of the cooled cookies. Sandwich with the remaining cookies.