Preheat oven to 350° F and cover a baking sheet with parchment paper.
Combine melted butter, egg, water, and cake mix. Mix with a large spoon.
Form into balls (about two-Tablespoon size), and assemble on a baking sheet. Bake for 8-10 minutes or just until edges are set.
Let cookies cool on a baking sheet for about 3 minutes, then transfer to a wire cooling rack.
In a medium-sized bowl, beat butter with a handheld mixer until it’s nice and fluffy. About 1 minute.
Add powdered sugar and milk, then mix on medium speed for another 1-2 minutes. Add vanilla.
When cookies have cooled, frost with buttercream frosting.