Place butter in a small saucepan over medium heat and heat until golden brown specks appear, swirling the pan occasionally. Butter will get foamy and if you swirl the pan around, you will see brown bits at the bottom and it will have a nutty smell. Remove from heat and pour into a small bowl. Make sure to get all those browned bits at the bottom of the pan, that is where all the flavor is. Allow to cool until it becomes solid (I refrigerate mine to speed up the process).
When brown butter is solid, preheat oven to 350 degrees. Cream together brown butter, brown sugar and sugar until light and fluffy. Add the egg, vanilla and milk and beat until combined. In a separate bowl, combine the flour, cornstarch, baking soda and salt and add to wet ingredients. Mix until just combined. Stir in one cup of M&M's. Chill dough for at least one hour or overnight.
Roll dough into balls, around 1 1/2 Tablespoons of dough per cookie. Press a few extra M&M's onto the top of each dough ball. Bake for 7- 9 minutes. Cookies will look underdone, but set up perfectly once they cool. My oven does bake slightly warmer than most and I think 7 minutes is perfect. Do not overbake or the cookies will be dry. Makes 24-30 cookies.