Mix together the cake mix, eggs, and oil in a large bowl. Roll the dough into balls the size of walnuts. Place 2 inches apart on ungreased baking sheets.
Bake in the preheated oven until the tops start to crack, about 8 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
In a large bowl combine cream cheese, butter, milk, and vanilla. Add the powdered sugar 1 cup at a time, mixing well with each addition. If consistency is too stiff, add more milk.
Spread a generous amount of icing on the bottom of a cookie, sandwich it with another cookie, pressing firmly so that the icing comes all the way out to the edge. Repeat with the remaining cookies.
Notes
Want to make these cookies even yummier? I added 1/2 cup sweetened flaked coconut to my frosting the second time I made them and it was so good. If you love coconut, I highly recommend it!