In a medium size bowl, mix together the flour, cocoa powder, sugar and melted butter. Press this mixture into the bottom of an 9" round (or 8x8 square) baking pan that has been sprayed with cooking spray. Bake at 325 degrees for 25 minutes.
Make the Chocolate Buttercream .
After the shortbread has cooled, spread the chocolate buttercream overtop the shortbread. Sprinkle the M&M's on top.
We like a thick layer of chocolate buttercream on top of our bars. If you'd like these bars to be less sweet, you can make a 1/2 recipe of buttercream for a thinner frosting layer.