Preheat the oven to 350°.
Using either a stand mixer or electric hand mixer, cream together the buttter and sugars until light in color and fluffy.
Scrape the sides and add in the eggs and vanilla. Mix well.
Add the flour, cocoa, baking powder, salt and cornstarch. Mix until thoroughly combined.
Double scoop the cookie dough onto a parchment lined cookie sheet. (Use two scoops to make one cookie)
Dip the bottom of a drinking glass into a small bowl of sugar and then carefully and slowly flatten the cookie dough. You may want to spray the bottom of the cup with non-stick spray before the first cookie.
Repeat with remaining cookies. Bake at 350° for 9-11 minutes. Cool completely.
While the cookies are cooling, mix together all of the ingredients for the frostiing until extremely smooth. You can thin the frositng out with just a tad of milk. A little will go a long way.
Once the cookies are completely cool, spread the frositng into the indent of the cookie.
Store in the fridge and serve cold.