Preheat the oven to 350 degrees.
In the bowl of an electric mixer, mix together the cake mix, the egg, melted butter, and vanilla extract until completely combined.
Use the 1/2 Tablespoon measure to scoop out portions and place them in the spaces in the mini muffin pan. Press them down inside each one so they are flat on top.
Bake for 5 to 6 minutes. Immediately after removing them from the oven, place the mini muffin pan on a cooling rack and use the rounded back of a teaspoon measure to make an indentation in the center of each one.
Allow them to cool inside the muffin pan just until they are easy to remove. To remove, run a butterknife around the outside of the mini muffin indentation and carefully pop it up.
Allow them to cool on a cooling rack completely.
Prepare the frosting by creaming together softened butter, powdered sugar, vanilla and just enough milk for thinning in the bowl of an electric mixer. Add the milk slowly, mixing in between. Add the green food coloring and mix until incorporated.
Add a little green frosting to the center of each cooled cookie, then sprinkle with Halloween round sprinkles. Store in an airtight container until ready to serve.