In a medium-sized mixing bowl, combine flours, cornstarch, salt, and baking soda. Whisk lightly until well mixed. Set aside.
In a stand mixer with a whisk attachment, cream together cold butter, brown sugar, and granulated sugar until well combined and smooth. About 3-4 minutes.
Add eggs one at a time and mix until smooth. Add vanilla and mix until combined.
Switch to paddle attachment and mix in flour mixture until smooth.
Add in M&Ms and chocolate chips and mix until just combined (or you can stir them in with a spoon by hand).
Using an ICE CREAM scoop (not a cookie scoop), scoop cookies into large balls (about 6-8 ounces each) and press extra M&Ms into the cookie dough balls (this makes it so the pretty M&Ms will show after baking).
Place dough balls on a baking sheet lined with parchment paper, cover, and chill in the refrigerator for at least 30 minutes. Note: If you don't have room to put a baking sheet in your refrigerator, just portion out the balls and place them on a plate, then transfer to baking sheet after refrigerating.
Heat oven to 425-degrees F. Bake in batches of 6 cookies (you can refrigerate them all on one baking sheet but don't bake them all at once). Place cookies in the oven and bake for 9-11 minutes (do not over bake).
Place cookies on a wire cooling rack and allow to cool at least 15 minutes before serving.
