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. If the dough is hard to work with refrigerate for about 15 minutes. Pinch of pieces of batter (about 1 tablespoon) and roll into balls. Place 1 inch apart on prepared cookie sheets and flatten slightly with fingertips. Bake for 8 to 10 minutes, until a slight indentation remains when lightly touched. Remove from the oven and slightly slam the cookie sheet on a surface. This helps flatten them. Immediately remove cookies from the cookie sheets with a spatula and cool on a wire rack. Let cookies cool completely.
In a small glass bowl, combine the cream cheese and butter until completely blended. Gradually add in the powdered sugar and vanilla and mix until the icing is fluffy and smooth. Spread half of the cookies with icing and top with remaining cookies. Store in the refrigerator in an airtight container or resealable plastic bags. Makes 2 dozen.