In a large bowl, whisk together the flour, cornstarch, baking soda, and salt until well-combined.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, cream cheese, brown sugar, and granulated sugar together until smoothly combined, wiping down the bowl and beater as needed. Add the whole egg and egg yolk one at a time, beating each in until incorporated. Mix in the vanilla extract until incorporated.
Add the dry ingredients to the wet and mix in on lowest speed just until partially combined, with the dough not yet even in texture. Add the M&M's and chopped chocolate and fold in with a flexible rubber spatula just until evenly dispersed into the dough, with no more streaks of dry ingredients still visible.
Transfer the dough to an airtight container and chill for at least 4 hours before baking (the cookie dough will keep in the refrigerator for at least one week).
To bake, preheat oven to 350ºF with an oven rack in the center position. Line a baking sheet with parchment paper.
Scoop the cookie dough by 2 1/4 ounce (about 1/4 cup) portions and roll into balls. Roll each ball between the palms of your hand to elongate into a tall cylinder-like mound, flattening the base to rest firmly on the lined baking tray. Space the mounds of cookie dough apart on the tray, with no more than 6 - 9 cookies on the tray at once. Press a few extra M&M's and pieces of chopped chocolate into the tops and sides of the cookies.
Bake cookies in the preheated oven for 11-13 minutes, or just until the cookies are puffed up and the tops no longer appear wet, rotating the tray halfway through the baking time. Don't overbake! Allow the cookies to cool on the baking sheet for about 10 minutes before transferring to a wire rack to cool completely. Store in an airtight container at room temperature.