Preheat oven to 350°F. Line a baking sheet with parchment paper.
In the bowl of a stand mixer, combine the butter, sugars, egg, and vanilla and beat on medium-speed until light and fluffy, about 3 to 4 minutes.
Add the flour, cornstarch, baking soda and salt, then mix until just combined.
Gently stir in 1 ¼ cups of the M&M's and all of the milk chocolate chips, reserving the remaining chocolate chips to place on top of the cookies before baking.
Scoop dough into balls and roll between the palms of your hands if you want very uniform-looking "perfect" cookies (or just drop onto the parchment-lined baking sheet in mounds, which is what I usually do). Press some of the reserved M&M's into the top of each cookie, then bake for 9-11 minutes, until the edges have set and the tops are just beginning to set, even if the cookies look slightly glossy and underbaked in the center.
Let the cookies cool on the baking sheet for 2-3 minutes before transferring to a wire cooling rack to cool completely.