Preheat oven to 350° F and line a 9" round cake pan with parchment paper and grease with cooking spray.
In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, cream the butter and sugars together until light and fluffy.
Add the eggs, one at a time, mixing well between each addition. Add in the vanilla.
Whisk the flour, baking soda, corn starch, and salt together in a medium bowl and add to the butter mixture and mix on low until just combined. Fold in the M&M's.
Transfer and press the cookie dough into an even layer in the prepared cake pan. Top with a few more M&M's, if desired.
Bake until the cookie is golden brown, about 25 minutes. Let the cookie cake cool in the pan completely before running a knife around the edge of the cake and transferring to a cake stand.
Prepare and transfer the frosting to a piping bag fitted with a large star tip. Pipe the frosting around the edge of the cooled cookie cake and top with additional M&M's. Slice into wedges.