Preheat oven to 350 degrees. Line cookie sheets with parchment paper.
In a large bowl combine the cake mix, eggs, and oil with a mixer. The batter will be very stiff. Pinch of pieces of batter and roll into 1 inch balls. Place 1 inch apart on prepared cookie sheets and flatten slightly with fingertips. Bake for 8 to 10 minutes. Remove immediately from the cookie sheets with a spatula and cool on a wire rack.
In a small glass bowl, combine the cream cheese and butter until completely blended. Gradually add in the powdered sugar and peppermint extract and mix until the icing is smooth. Color frosting green or red if desired. Spread half of the cookies with icing and top with remaining cookies.
Roll in sprinkles, crushed candy canes, or just leave them plain.
Store in the refrigerator in an airtight container or resealable plastic bags. Makes 2 dozen cookies.