Combine the cake mix, butter, milk and egg in the bowl of an electric mixer and blend until smooth. Using a cookie scoop or small ice cream scoop, drop the batter onto a cookie sheet, leaving two inches between each cookie.
Bake for 10-12 minutes, or until golden. Let the cookies cool for one minute, then transfer to a wire rack to cool completely.
Spread some frosting onto the bottom side of one cookie and top with another cookie, creating a little sandwich with the frosting. Roll the edges of the cookie in the sprinkles.