In a large mixing bowl, combine butter and sugar, beating until light and fluffy.
Add egg and water, beating until combined.
Add cake mix, and beat until combined. Dough will be thick.
Cover and refrigerate for 2-3 hours, or until it can be rolled into balls.
Coat non-stick mini muffin pans with cooking spray.
Roll dough into scant 1-inch balls, about 1 1/2 - 2 tsp. dough, and place in the bottom of each muffin cup.
Make an indentation with your thumb in the center of each dough ball.
Bake at 350 degrees for 8-10 minutes, or until edges are pale golden brown.
Immediately remove heat, and use the end of a wooden spoon to re-indent the center of each cup.
Allow to cool completely before removing to a wire rack. They're a little delicate to remove from the pans, so make sure you're careful, and it helps to sort of spin them out of the cup!
Meanwhile, prepare buttercream.